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Номер 2, страница 440 - гдз по физике 10 класс учебник Касьянов
Авторы: Касьянов В. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2021 - 2026
Уровень обучения: углублённый
Цвет обложки: белый самолет и молнии изображены
ISBN: 978-5-09-103621-3
Популярные ГДЗ в 10 классе
Лабораторные работы. 2. Изучение движения тела, брошенного горизонтально. Задание 1 - номер 2, страница 440.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390546 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "440" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-1-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1187 #items: array:3 [ 0 => App\Models\Branch {#1071 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Book {#1075 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1074} "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1072} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1105} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1106 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "438" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1109 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Branch {#1140 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1142 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 …2} ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "426" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1142 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1107} "field_page_start" => "438" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1108} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1144 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389655 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 1" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "439" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1147 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1150 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1150 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Branch {#1178 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_page_start" => "438" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1180 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1181 …2} ] #original: array:24 [ "id" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_page_start" => "438" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1180 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1181 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389655 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 1" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145} "field_page_start" => "439" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1203 #items: array:2 [ 0 => App\Models\Element {#1188 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1640883 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:1 [ 0 => App\Models\Edition {#1186 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1390546" "type" => "task" ] "text" => "<p><strong>2.</strong> Используя уравнения (1), (2) и зная $v_{0 \text{ ср}}$, найдите координаты $\text{x}$ и $\text{y}$ шарика через каждые 0,05 с. Постройте расчётную траекторию движения на листе бумаги, прикреплённом к вертикальной фанерной доске. Для удобства используйте таблицу 30, в которой координата $\text{y}$ уже подсчитана.</p><p><strong>Таблица 30</strong></p><p>Времена $\text{t}$ (с): $0$, $0,05$, $0,10$, $0,15$, $0,2$</p><p>Соответствующие координаты $\text{y}$ (м): $0$, $0,012$, $0,049$, $0,11$, $0,196$</p><p>Координаты $\text{x}$ (м) в таблице не указаны.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1711" "height" => 652 "path" => "/media/fizika_10/kasyanov-u/0-lab02-1/2-1.webp?ts=1757958219" ] ] ] #original: array:7 [ "id" => 1640883 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1189} "task" => array:2 [ "refs" => "1390546" "type" => "task" ] "text" => "<p><strong>2.</strong> Используя уравнения (1), (2) и зная $v_{0 \text{ ср}}$, найдите координаты $\text{x}$ и $\text{y}$ шарика через каждые 0,05 с. Постройте расчётную траекторию движения на листе бумаги, прикреплённом к вертикальной фанерной доске. Для удобства используйте таблицу 30, в которой координата $\text{y}$ уже подсчитана.</p><p><strong>Таблица 30</strong></p><p>Времена $\text{t}$ (с): $0$, $0,05$, $0,10$, $0,15$, $0,2$</p><p>Соответствующие координаты $\text{y}$ (м): $0$, $0,012$, $0,049$, $0,11$, $0,196$</p><p>Координаты $\text{x}$ (м) в таблице не указаны.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1711" "height" => 652 "path" => "/media/fizika_10/kasyanov-u/0-lab02-1/2-1.webp?ts=1757958219" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1195 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1693558 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:1 [ 0 => App\Models\Edition {#1197 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1390546" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Временные отметки, $t$, с: 0; 0,05; 0,10; 0,15; 0,2.<br>Вертикальные координаты, $y$, м: 0; 0,012; 0,049; 0,11; 0,196.<br>Движение начинается из начала координат $(0, 0)$.<br>Начальная скорость направлена горизонтально, $v_{0y} = 0$.<br>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>Горизонтальные координаты $x$ для каждого момента времени $t$.<br>Построить траекторию движения шарика $y(x)$.</p><p><strong>Решение:</strong></p><p>Движение шарика, брошенного горизонтально, можно разложить на два независимых движения: равномерное по горизонтали (ось Ox) и равноускоренное по вертикали (ось Oy).</p><p><strong>1.</strong> Движение по горизонтали описывается уравнением (1), упомянутым в задаче: $x(t) = v_{0 ср} \cdot t$ где $v_{0 ср}$ — средняя начальная скорость, направленная горизонтально.</p><p><strong>2.</strong> Движение по вертикали описывается уравнением (2): $y(t) = \frac{gt^2}{2}$ где $g$ — ускорение свободного падения (примем $g \approx 9,8 \, м/с^2$). Координаты $y$ уже рассчитаны в таблице по этой формуле.</p><p>В условии задачи указано, что средняя начальная скорость $v_{0 ср}$ известна. Поскольку ее числовое значение не приведено, для выполнения расчетов и построения графика необходимо задать это значение. Предположим, что из предыдущих измерений было найдено, что $v_{0 ср} = 1,5 \, м/с$.</p><p>Теперь, используя уравнение (1), рассчитаем значения координаты $x$ для каждого момента времени из таблицы:</p><ul><li>При $t = 0$ с: $x = 1,5 \, м/с \cdot 0 \, с = 0 \, м$</li><li>При $t = 0,05$ с: $x = 1,5 \, м/с \cdot 0,05 \, с = 0,075 \, м$</li><li>При $t = 0,10$ с: $x = 1,5 \, м/с \cdot 0,10 \, с = 0,150 \, м$</li><li>При $t = 0,15$ с: $x = 1,5 \, м/с \cdot 0,15 \, с = 0,225 \, м$</li><li>При $t = 0,20$ с: $x = 1,5 \, м/с \cdot 0,20 \, с = 0,300 \, м$</li></ul><p>Заполним строку $x$, м в таблице 30 полученными значениями:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center; padding: 5px;"><strong>t, с</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,05</td><td style="text-align: center; padding: 5px;">0,10</td><td style="text-align: center; padding: 5px;">0,15</td><td style="text-align: center; padding: 5px;">0,2</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>y, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,012</td><td style="text-align: center; padding: 5px;">0,049</td><td style="text-align: center; padding: 5px;">0,11</td><td style="text-align: center; padding: 5px;">0,196</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>x, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,075</td><td style="text-align: center; padding: 5px;">0,150</td><td style="text-align: center; padding: 5px;">0,225</td><td style="text-align: center; padding: 5px;">0,300</td></tr></tbody></table><p>Для построения расчётной траектории движения на листе бумаги необходимо:</p><ol><li>Начертить систему координат Oxy. Начало координат $(0,0)$ — точка старта шарика.</li><li>Направить ось Ox горизонтально вправо, а ось Oy — вертикально вниз (так как значения $y$ положительны).</li><li>Выбрать удобный масштаб для обеих осей. Например, по оси Ox 10 см может соответствовать 0,3 м, а по оси Oy 10 см может соответствовать 0,2 м.</li><li>Отметить на координатной плоскости точки с полученными координатами $(x, y)$: <ul><li>$(0; 0)$</li><li>$(0,075; 0,012)$</li><li>$(0,150; 0,049)$</li><li>$(0,225; 0,11)$</li><li>$(0,300; 0,196)$</li></ul></li><li>Соединить отмеченные точки плавной линией. Полученная кривая является параболой и представляет собой траекторию движения шарика.</li></ol><p><strong>Ответ:</strong></p><p>При условии, что начальная скорость шарика $v_{0 ср} = 1,5 \, м/с$, координаты $x$ в соответствующие моменты времени равны:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center; padding: 5px;"><strong>t, с</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,05</td><td style="text-align: center; padding: 5px;">0,10</td><td style="text-align: center; padding: 5px;">0,15</td><td style="text-align: center; padding: 5px;">0,2</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>y, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,012</td><td style="text-align: center; padding: 5px;">0,049</td><td style="text-align: center; padding: 5px;">0,11</td><td style="text-align: center; padding: 5px;">0,196</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>x, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,075</td><td style="text-align: center; padding: 5px;">0,150</td><td style="text-align: center; padding: 5px;">0,225</td><td style="text-align: center; padding: 5px;">0,300</td></tr></tbody></table><p>Траектория движения строится на графике по точкам с координатами $(x, y)$, взятыми из таблицы.</p>" ] #original: array:6 [ "id" => 1693558 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1196} "task" => array:2 [ "refs" => "1390546" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Временные отметки, $t$, с: 0; 0,05; 0,10; 0,15; 0,2.<br>Вертикальные координаты, $y$, м: 0; 0,012; 0,049; 0,11; 0,196.<br>Движение начинается из начала координат $(0, 0)$.<br>Начальная скорость направлена горизонтально, $v_{0y} = 0$.<br>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>Горизонтальные координаты $x$ для каждого момента времени $t$.<br>Построить траекторию движения шарика $y(x)$.</p><p><strong>Решение:</strong></p><p>Движение шарика, брошенного горизонтально, можно разложить на два независимых движения: равномерное по горизонтали (ось Ox) и равноускоренное по вертикали (ось Oy).</p><p><strong>1.</strong> Движение по горизонтали описывается уравнением (1), упомянутым в задаче: $x(t) = v_{0 ср} \cdot t$ где $v_{0 ср}$ — средняя начальная скорость, направленная горизонтально.</p><p><strong>2.</strong> Движение по вертикали описывается уравнением (2): $y(t) = \frac{gt^2}{2}$ где $g$ — ускорение свободного падения (примем $g \approx 9,8 \, м/с^2$). Координаты $y$ уже рассчитаны в таблице по этой формуле.</p><p>В условии задачи указано, что средняя начальная скорость $v_{0 ср}$ известна. Поскольку ее числовое значение не приведено, для выполнения расчетов и построения графика необходимо задать это значение. Предположим, что из предыдущих измерений было найдено, что $v_{0 ср} = 1,5 \, м/с$.</p><p>Теперь, используя уравнение (1), рассчитаем значения координаты $x$ для каждого момента времени из таблицы:</p><ul><li>При $t = 0$ с: $x = 1,5 \, м/с \cdot 0 \, с = 0 \, м$</li><li>При $t = 0,05$ с: $x = 1,5 \, м/с \cdot 0,05 \, с = 0,075 \, м$</li><li>При $t = 0,10$ с: $x = 1,5 \, м/с \cdot 0,10 \, с = 0,150 \, м$</li><li>При $t = 0,15$ с: $x = 1,5 \, м/с \cdot 0,15 \, с = 0,225 \, м$</li><li>При $t = 0,20$ с: $x = 1,5 \, м/с \cdot 0,20 \, с = 0,300 \, м$</li></ul><p>Заполним строку $x$, м в таблице 30 полученными значениями:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center; padding: 5px;"><strong>t, с</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,05</td><td style="text-align: center; padding: 5px;">0,10</td><td style="text-align: center; padding: 5px;">0,15</td><td style="text-align: center; padding: 5px;">0,2</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>y, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,012</td><td style="text-align: center; padding: 5px;">0,049</td><td style="text-align: center; padding: 5px;">0,11</td><td style="text-align: center; padding: 5px;">0,196</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>x, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,075</td><td style="text-align: center; padding: 5px;">0,150</td><td style="text-align: center; padding: 5px;">0,225</td><td style="text-align: center; padding: 5px;">0,300</td></tr></tbody></table><p>Для построения расчётной траектории движения на листе бумаги необходимо:</p><ol><li>Начертить систему координат Oxy. Начало координат $(0,0)$ — точка старта шарика.</li><li>Направить ось Ox горизонтально вправо, а ось Oy — вертикально вниз (так как значения $y$ положительны).</li><li>Выбрать удобный масштаб для обеих осей. Например, по оси Ox 10 см может соответствовать 0,3 м, а по оси Oy 10 см может соответствовать 0,2 м.</li><li>Отметить на координатной плоскости точки с полученными координатами $(x, y)$: <ul><li>$(0; 0)$</li><li>$(0,075; 0,012)$</li><li>$(0,150; 0,049)$</li><li>$(0,225; 0,11)$</li><li>$(0,300; 0,196)$</li></ul></li><li>Соединить отмеченные точки плавной линией. Полученная кривая является параболой и представляет собой траекторию движения шарика.</li></ol><p><strong>Ответ:</strong></p><p>При условии, что начальная скорость шарика $v_{0 ср} = 1,5 \, м/с$, координаты $x$ в соответствующие моменты времени равны:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center; padding: 5px;"><strong>t, с</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,05</td><td style="text-align: center; padding: 5px;">0,10</td><td style="text-align: center; padding: 5px;">0,15</td><td style="text-align: center; padding: 5px;">0,2</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>y, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,012</td><td style="text-align: center; padding: 5px;">0,049</td><td style="text-align: center; padding: 5px;">0,11</td><td style="text-align: center; padding: 5px;">0,196</td></tr><tr><td style="text-align: center; padding: 5px;"><strong>x, м</strong></td><td style="text-align: center; padding: 5px;">0</td><td style="text-align: center; padding: 5px;">0,075</td><td style="text-align: center; padding: 5px;">0,150</td><td style="text-align: center; padding: 5px;">0,225</td><td style="text-align: center; padding: 5px;">0,300</td></tr></tbody></table><p>Траектория движения строится на графике по точкам с координатами $(x, y)$, взятыми из таблицы.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390547" "type" => "task" ] "previous" => array:2 [ "refs" => "1390545" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ 0 => App\Models\Book {#1205 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Term {#1204 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:1 [ 0 => App\Models\Term {#1208 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1209 #items: array:1 [ 0 => App\Models\Term {#1210 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Term {#1212 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1213 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ 0 => App\Models\Term {#1215 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ 0 => App\Models\Term {#1217 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:1 [ 0 => App\Models\Term {#1219 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1220 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1221 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:1 [ 0 => App\Models\Term {#1223 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:1 [ 0 => App\Models\Term {#1225 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" …6 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:1 [ 0 => App\Models\Term {#1227 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1228 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1229 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1230 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1231 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ 0 => App\Models\Term {#1233 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1206} "field_class" => Illuminate\Database\Eloquent\Collection {#1207} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1209} "field_author" => Illuminate\Database\Eloquent\Collection {#1211} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1213} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1214} "field_country" => Illuminate\Database\Eloquent\Collection {#1216} "field_city" => Illuminate\Database\Eloquent\Collection {#1218} "field_series" => Illuminate\Database\Eloquent\Collection {#1220} "field_umk" => Illuminate\Database\Eloquent\Collection {#1221} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1222} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1224} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1226} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1228} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1229} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1230} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1231} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1232} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1405 #items: array:1 [ 0 => App\Models\BookPage {#333 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1391088 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "440" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-440" "field_display_title" => "440" "field_folder" => "1" "field_image_name" => "440" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1026 #items: array:1 [ 0 => App\Models\Book {#1234 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:1 [ 0 => App\Models\Element {#1267 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1391089" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391087" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:8 [ 0 => App\Models\Task {#1276 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1314 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1325 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1336 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1359 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1370 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1381 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1392 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1391088 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "440" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-440" "field_display_title" => "440" "field_folder" => "1" "field_image_name" => "440" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1026} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265} "content" => Illuminate\Database\Eloquent\Collection {#1266} "next" => array:2 [ "refs" => "1391089" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391087" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1275} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1390546 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "440" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-1-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1187} "content" => Illuminate\Database\Eloquent\Collection {#1203} "next" => array:2 [ "refs" => "1390547" "type" => "task" ] "previous" => array:2 [ "refs" => "1390545" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1236} "page" => array:2 [ "refs" => "1391088" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№2 (с. 440)
Условие. №2 (с. 440)
скриншот условия
2. Используя уравнения (1), (2) и зная $v_{0 \text{ ср}}$, найдите координаты $\text{x}$ и $\text{y}$ шарика через каждые 0,05 с. Постройте расчётную траекторию движения на листе бумаги, прикреплённом к вертикальной фанерной доске. Для удобства используйте таблицу 30, в которой координата $\text{y}$ уже подсчитана.
Таблица 30
Времена $\text{t}$ (с): $0$, $0,05$, $0,10$, $0,15$, $0,2$
Соответствующие координаты $\text{y}$ (м): $0$, $0,012$, $0,049$, $0,11$, $0,196$
Координаты $\text{x}$ (м) в таблице не указаны.
Решение. №2 (с. 440)
Дано:
Временные отметки, $t$, с: 0; 0,05; 0,10; 0,15; 0,2.
Вертикальные координаты, $y$, м: 0; 0,012; 0,049; 0,11; 0,196.
Движение начинается из начала координат $(0, 0)$.
Начальная скорость направлена горизонтально, $v_{0y} = 0$.
Все данные представлены в системе СИ.
Найти:
Горизонтальные координаты $x$ для каждого момента времени $t$.
Построить траекторию движения шарика $y(x)$.
Решение:
Движение шарика, брошенного горизонтально, можно разложить на два независимых движения: равномерное по горизонтали (ось Ox) и равноускоренное по вертикали (ось Oy).
1. Движение по горизонтали описывается уравнением (1), упомянутым в задаче: $x(t) = v_{0 ср} \cdot t$ где $v_{0 ср}$ — средняя начальная скорость, направленная горизонтально.
2. Движение по вертикали описывается уравнением (2): $y(t) = \frac{gt^2}{2}$ где $g$ — ускорение свободного падения (примем $g \approx 9,8 \, м/с^2$). Координаты $y$ уже рассчитаны в таблице по этой формуле.
В условии задачи указано, что средняя начальная скорость $v_{0 ср}$ известна. Поскольку ее числовое значение не приведено, для выполнения расчетов и построения графика необходимо задать это значение. Предположим, что из предыдущих измерений было найдено, что $v_{0 ср} = 1,5 \, м/с$.
Теперь, используя уравнение (1), рассчитаем значения координаты $x$ для каждого момента времени из таблицы:
- При $t = 0$ с: $x = 1,5 \, м/с \cdot 0 \, с = 0 \, м$
- При $t = 0,05$ с: $x = 1,5 \, м/с \cdot 0,05 \, с = 0,075 \, м$
- При $t = 0,10$ с: $x = 1,5 \, м/с \cdot 0,10 \, с = 0,150 \, м$
- При $t = 0,15$ с: $x = 1,5 \, м/с \cdot 0,15 \, с = 0,225 \, м$
- При $t = 0,20$ с: $x = 1,5 \, м/с \cdot 0,20 \, с = 0,300 \, м$
Заполним строку $x$, м в таблице 30 полученными значениями:
| t, с | 0 | 0,05 | 0,10 | 0,15 | 0,2 |
| y, м | 0 | 0,012 | 0,049 | 0,11 | 0,196 |
| x, м | 0 | 0,075 | 0,150 | 0,225 | 0,300 |
Для построения расчётной траектории движения на листе бумаги необходимо:
- Начертить систему координат Oxy. Начало координат $(0,0)$ — точка старта шарика.
- Направить ось Ox горизонтально вправо, а ось Oy — вертикально вниз (так как значения $y$ положительны).
- Выбрать удобный масштаб для обеих осей. Например, по оси Ox 10 см может соответствовать 0,3 м, а по оси Oy 10 см может соответствовать 0,2 м.
- Отметить на координатной плоскости точки с полученными координатами $(x, y)$:
- $(0; 0)$
- $(0,075; 0,012)$
- $(0,150; 0,049)$
- $(0,225; 0,11)$
- $(0,300; 0,196)$
- Соединить отмеченные точки плавной линией. Полученная кривая является параболой и представляет собой траекторию движения шарика.
Ответ:
При условии, что начальная скорость шарика $v_{0 ср} = 1,5 \, м/с$, координаты $x$ в соответствующие моменты времени равны:
| t, с | 0 | 0,05 | 0,10 | 0,15 | 0,2 |
| y, м | 0 | 0,012 | 0,049 | 0,11 | 0,196 |
| x, м | 0 | 0,075 | 0,150 | 0,225 | 0,300 |
Траектория движения строится на графике по точкам с координатами $(x, y)$, взятыми из таблицы.
Другие задания:
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