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Номер 1, 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 2 - номер 1, страница 440.
App\Models\Task {#1024 // 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" => 1390549 "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/lab02-2-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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 {#333 #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 {#1033 #items: array:1 [ 0 => App\Models\Book {#1030 #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 {#1032 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1035 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 …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 {#1057 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 …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 {#1032 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1035 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 …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 {#1057 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 …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 {#1062 #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 {#333} "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 {#1033} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062} ] #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 {#1063 #items: array:3 [ 0 => App\Models\Branch {#1064 #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 {#1065 #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 {#1066 #items: array:1 [ 0 => App\Models\Book {#1067 #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 {#1068 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1091 …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 {#1092 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1095 …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 {#1068 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1091 …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 {#1092 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1095 …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 {#1097 #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 {#1065} "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 {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1097} ] #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 {#1098 #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 {#1099 #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 {#1100 #items: array:1 [ 0 => App\Models\Book {#1101 #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 {#1102 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1111 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1125 …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 {#1126 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1129 …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 {#1102 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1111 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1125 …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 {#1126 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1129 …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 {#1131 #items: array:1 [ 0 => App\Models\Branch {#1132 #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 {#1133 …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 {#1134 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1135 …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 {#1133 …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 {#1134 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1135 …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 {#1099} "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 {#1100} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1131} ] #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 {#1136 #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" => 1389656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 2" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "440" "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 {#1138 #items: array:1 [ 0 => App\Models\Book {#1139 #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 {#1140 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1149 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1151 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1153 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1163 …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 {#1164 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1167 …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 {#1140 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1149 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1151 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1153 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1163 …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 {#1164 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1167 …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 {#1169 #items: array:1 [ 0 => App\Models\Branch {#1170 #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 {#1171 …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 {#1172 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1173 …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 {#1171 …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 {#1172 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1173 …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" => 1389656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 2" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "440" "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 {#1138} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1169} ] #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 {#1178 #items: array:2 [ 0 => App\Models\Element {#1179 #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" => 1640887 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\Edition {#1181 #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 {#1182 …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 {#1184 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1186 …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 {#1182 …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 {#1184 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1186 …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" => "1390549" "type" => "task" ] "text" => "<p><strong>Задание 2.</strong> Разработать способ измерения начальной скорости шарика, брошенного горизонтально.</p><p><strong>1.</strong> Соберите экспериментальную установку (см. рис. 345), устанавливая высоту вылета шарика $h = 196 \text{ мм}$ (для упрощения расчётов). При измерении $\text{h}$ линейкой с миллиметровыми делениями можно принять, что максимальная абсолютная погрешность $\Delta h = 1 \text{ мм}$, т. е.</p><p>$h = (196 \pm 1) \text{ мм}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1725" "height" => 496 "path" => "/media/fizika_10/kasyanov-u/0-lab02-2/1-1.webp?ts=1757958219" ] ] ] #original: array:7 [ "id" => 1640887 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1180} "task" => array:2 [ "refs" => "1390549" "type" => "task" ] "text" => "<p><strong>Задание 2.</strong> Разработать способ измерения начальной скорости шарика, брошенного горизонтально.</p><p><strong>1.</strong> Соберите экспериментальную установку (см. рис. 345), устанавливая высоту вылета шарика $h = 196 \text{ мм}$ (для упрощения расчётов). При измерении $\text{h}$ линейкой с миллиметровыми делениями можно принять, что максимальная абсолютная погрешность $\Delta h = 1 \text{ мм}$, т. е.</p><p>$h = (196 \pm 1) \text{ мм}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1725" "height" => 496 "path" => "/media/fizika_10/kasyanov-u/0-lab02-2/1-1.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 {#1187 #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" => 1693561 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Edition {#1189 #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 {#1190 …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 {#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" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …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 {#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" => "1390549" "type" => "task" ] "text" => "<p>Способ измерения начальной скорости шарика, брошенного горизонтально, основывается на принципе независимости движений. Движение шарика рассматривается как результат сложения двух независимых движений: равномерного прямолинейного движения в горизонтальном направлении и равноускоренного движения (свободного падения) в вертикальном направлении.</p><p>Для определения начальной скорости необходимо выполнить следующие шаги:</p><p><strong>1.</strong> Собрать экспериментальную установку, например, используя наклонный желоб, установленный на краю стола, так, чтобы шарик в момент отрыва двигался строго горизонтально. Установить и измерить с помощью линейки высоту вылета шарика $h$ от точки старта до поверхности, на которую он будет падать. Согласно заданию, для упрощения расчетов эта высота принимается равной $h = 196$ мм. Принимая во внимание, что измерение производится линейкой с миллиметровыми делениями, максимальная абсолютная погрешность $\Delta h = 1$ мм, то есть $h = (196 \pm 1)$ мм.</p><p><strong>2.</strong> Определить и отметить на полу точку, находящуюся строго под точкой вылета шарика. Это можно сделать с помощью отвеса. Эта точка будет служить началом отсчета для измерения дальности полета. В предполагаемое место падения шарика следует положить лист белой бумаги, а на него — лист копировальной бумаги. Это позволит точно зафиксировать точку приземления шарика.</p><p><strong>3.</strong> Произвести запуск шарика. Важно запускать его каждый раз с одной и той же высоты на наклонном желобе, чтобы начальная скорость была одинаковой. После падения шарика на бумаге останется четкий след. Измерить с помощью линейки или рулетки дальность полета $L$ — расстояние по горизонтали от начальной точки отсчета до следа от падения шарика.</p><p><strong>4.</strong> Для уменьшения влияния случайных погрешностей и получения более точного результата эксперимент следует повторить несколько раз (например, 3-5 раз). Каждый раз измеряя дальность полета $L_i$, а затем рассчитать среднее значение дальности полета $\bar{L}$.</p><p><strong>5.</strong> Используя измеренные значения, рассчитать начальную скорость шарика $v_0$ по расчетной формуле, вывод которой представлен ниже.</p><p><strong>Дано:</strong><br>Высота вылета шарика $h = (196 \pm 1)$ мм.<br>Ускорение свободного падения $g \approx 9.8$ м/с<sup>2</sup>.<br><br><i>Перевод в систему СИ:</i><br>$h = (0.196 \pm 0.001)$ м.</p><p><strong>Найти:</strong><br>Начальную скорость шарика $v_0$.</p><p><strong>Решение:</strong><br>Рассмотрим движение шарика по двум осям. Ось OX направим горизонтально в сторону полета, а ось OY — вертикально вниз. Начало координат поместим в точку вылета шарика.<br><br>Движение по горизонтали (ось OX) является равномерным, так как сила тяжести действует вертикально и не влияет на горизонтальную составляющую скорости. Уравнение движения:<br>$x(t) = v_0 t$<br><br>Движение по вертикали (ось OY) является равноускоренным (свободное падение), так как начальная вертикальная скорость равна нулю. Уравнение движения:<br>$y(t) = \frac{gt^2}{2}$<br><br>В момент падения шарик преодолеет по вертикали расстояние $h$, а по горизонтали — расстояние $L$ (дальность полета). Время полета $t_{пол}$ можно найти из уравнения для вертикального движения, подставив $y(t_{пол}) = h$:<br>$h = \frac{gt_{пол}^2}{2}$<br>Выразим отсюда время полета:<br>$t_{пол} = \sqrt{\frac{2h}{g}}$<br><br>За это же время шарик пролетит по горизонтали расстояние $L$. Подставим время полета в уравнение для горизонтального движения $L = x(t_{пол})$:<br>$L = v_0 t_{пол} = v_0 \sqrt{\frac{2h}{g}}$<br><br>Из этого соотношения выразим искомую начальную скорость $v_0$:<br>$v_0 = \frac{L}{\sqrt{\frac{2h}{g}}} = L \sqrt{\frac{g}{2h}}$<br><br>Это и есть расчетная формула. Для вычисления $v_0$ необходимо экспериментально измерить дальность полета $L$.<br>Вычислим время полета для заданной высоты, чтобы продемонстрировать упрощение расчетов:<br>$t_{пол} = \sqrt{\frac{2 \cdot 0.196 \, м}{9.8 \, м/с^2}} = \sqrt{\frac{0.392}{9.8} \, с^2} = \sqrt{0.04 \, с^2} = 0.2 \, с$<br><br>Тогда формула для расчета начальной скорости для данной установки принимает вид:<br>$v_0 = \frac{L}{0.2 \, с} = 5L$<br>Таким образом, измерив дальность полета $L$ в метрах и умножив ее на 5, можно найти начальную скорость $v_0$ в м/с.</p><p><strong>Ответ:</strong> Способ измерения начальной скорости шарика заключается в следующем: необходимо измерить высоту вылета шарика $h$ и горизонтальную дальность его полета $L$. Начальная скорость рассчитывается по формуле $v_0 = L \sqrt{\frac{g}{2h}}$. При заданной высоте $h = 196$ мм, время полета составляет $t \approx 0.2$ с, и для нахождения начальной скорости (в м/с) достаточно измерить дальность полета $L$ (в м) и умножить это значение на 5.</p>" ] #original: array:6 [ "id" => 1693561 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1188} "task" => array:2 [ "refs" => "1390549" "type" => "task" ] "text" => "<p>Способ измерения начальной скорости шарика, брошенного горизонтально, основывается на принципе независимости движений. Движение шарика рассматривается как результат сложения двух независимых движений: равномерного прямолинейного движения в горизонтальном направлении и равноускоренного движения (свободного падения) в вертикальном направлении.</p><p>Для определения начальной скорости необходимо выполнить следующие шаги:</p><p><strong>1.</strong> Собрать экспериментальную установку, например, используя наклонный желоб, установленный на краю стола, так, чтобы шарик в момент отрыва двигался строго горизонтально. Установить и измерить с помощью линейки высоту вылета шарика $h$ от точки старта до поверхности, на которую он будет падать. Согласно заданию, для упрощения расчетов эта высота принимается равной $h = 196$ мм. Принимая во внимание, что измерение производится линейкой с миллиметровыми делениями, максимальная абсолютная погрешность $\Delta h = 1$ мм, то есть $h = (196 \pm 1)$ мм.</p><p><strong>2.</strong> Определить и отметить на полу точку, находящуюся строго под точкой вылета шарика. Это можно сделать с помощью отвеса. Эта точка будет служить началом отсчета для измерения дальности полета. В предполагаемое место падения шарика следует положить лист белой бумаги, а на него — лист копировальной бумаги. Это позволит точно зафиксировать точку приземления шарика.</p><p><strong>3.</strong> Произвести запуск шарика. Важно запускать его каждый раз с одной и той же высоты на наклонном желобе, чтобы начальная скорость была одинаковой. После падения шарика на бумаге останется четкий след. Измерить с помощью линейки или рулетки дальность полета $L$ — расстояние по горизонтали от начальной точки отсчета до следа от падения шарика.</p><p><strong>4.</strong> Для уменьшения влияния случайных погрешностей и получения более точного результата эксперимент следует повторить несколько раз (например, 3-5 раз). Каждый раз измеряя дальность полета $L_i$, а затем рассчитать среднее значение дальности полета $\bar{L}$.</p><p><strong>5.</strong> Используя измеренные значения, рассчитать начальную скорость шарика $v_0$ по расчетной формуле, вывод которой представлен ниже.</p><p><strong>Дано:</strong><br>Высота вылета шарика $h = (196 \pm 1)$ мм.<br>Ускорение свободного падения $g \approx 9.8$ м/с<sup>2</sup>.<br><br><i>Перевод в систему СИ:</i><br>$h = (0.196 \pm 0.001)$ м.</p><p><strong>Найти:</strong><br>Начальную скорость шарика $v_0$.</p><p><strong>Решение:</strong><br>Рассмотрим движение шарика по двум осям. Ось OX направим горизонтально в сторону полета, а ось OY — вертикально вниз. Начало координат поместим в точку вылета шарика.<br><br>Движение по горизонтали (ось OX) является равномерным, так как сила тяжести действует вертикально и не влияет на горизонтальную составляющую скорости. Уравнение движения:<br>$x(t) = v_0 t$<br><br>Движение по вертикали (ось OY) является равноускоренным (свободное падение), так как начальная вертикальная скорость равна нулю. Уравнение движения:<br>$y(t) = \frac{gt^2}{2}$<br><br>В момент падения шарик преодолеет по вертикали расстояние $h$, а по горизонтали — расстояние $L$ (дальность полета). Время полета $t_{пол}$ можно найти из уравнения для вертикального движения, подставив $y(t_{пол}) = h$:<br>$h = \frac{gt_{пол}^2}{2}$<br>Выразим отсюда время полета:<br>$t_{пол} = \sqrt{\frac{2h}{g}}$<br><br>За это же время шарик пролетит по горизонтали расстояние $L$. Подставим время полета в уравнение для горизонтального движения $L = x(t_{пол})$:<br>$L = v_0 t_{пол} = v_0 \sqrt{\frac{2h}{g}}$<br><br>Из этого соотношения выразим искомую начальную скорость $v_0$:<br>$v_0 = \frac{L}{\sqrt{\frac{2h}{g}}} = L \sqrt{\frac{g}{2h}}$<br><br>Это и есть расчетная формула. Для вычисления $v_0$ необходимо экспериментально измерить дальность полета $L$.<br>Вычислим время полета для заданной высоты, чтобы продемонстрировать упрощение расчетов:<br>$t_{пол} = \sqrt{\frac{2 \cdot 0.196 \, м}{9.8 \, м/с^2}} = \sqrt{\frac{0.392}{9.8} \, с^2} = \sqrt{0.04 \, с^2} = 0.2 \, с$<br><br>Тогда формула для расчета начальной скорости для данной установки принимает вид:<br>$v_0 = \frac{L}{0.2 \, с} = 5L$<br>Таким образом, измерив дальность полета $L$ в метрах и умножив ее на 5, можно найти начальную скорость $v_0$ в м/с.</p><p><strong>Ответ:</strong> Способ измерения начальной скорости шарика заключается в следующем: необходимо измерить высоту вылета шарика $h$ и горизонтальную дальность его полета $L$. Начальная скорость рассчитывается по формуле $v_0 = L \sqrt{\frac{g}{2h}}$. При заданной высоте $h = 196$ мм, время полета составляет $t \approx 0.2$ с, и для нахождения начальной скорости (в м/с) достаточно измерить дальность полета $L$ (в м) и умножить это значение на 5.</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" => "1390550" "type" => "task" ] "previous" => array:2 [ "refs" => "1390548" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1196 #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 {#1197 #items: array:1 [ 0 => App\Models\Term {#1198 #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 {#1199 #items: array:1 [ 0 => App\Models\Term {#1200 #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 {#1201 #items: array:1 [ 0 => App\Models\Term {#1202 #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 {#1203 #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: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 {#1205 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Term {#1207 #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 {#1208 #items: array:1 [ 0 => App\Models\Term {#1209 #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 {#1210 #items: array:1 [ 0 => App\Models\Term {#1211 #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 {#1212 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1213 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => 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: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 {#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: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 {#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 [ …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 {#1220 #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 {#1221 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1222 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1223 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => 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: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 {#1197} "field_class" => Illuminate\Database\Eloquent\Collection {#1199} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1201} "field_author" => Illuminate\Database\Eloquent\Collection {#1203} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1205} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1206} "field_country" => Illuminate\Database\Eloquent\Collection {#1208} "field_city" => Illuminate\Database\Eloquent\Collection {#1210} "field_series" => Illuminate\Database\Eloquent\Collection {#1212} "field_umk" => Illuminate\Database\Eloquent\Collection {#1213} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1214} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1216} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1218} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1220} "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 {#1221} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1222} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1223} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1224} "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 {#1404 #items: array:1 [ 0 => App\Models\BookPage {#1230 #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 {#1233 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1232 #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 {#1264 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Element {#1266 #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 {#1274 #items: array:8 [ 0 => App\Models\Task {#1275 #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 {#1313 #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 {#1324 #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 {#1335 #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 {#1358 #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 {#1369 #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 {#1380 #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 {#1391 #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: [] 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№1 (с. 440)
Условие. №1 (с. 440)
скриншот условия
Задание 2. Разработать способ измерения начальной скорости шарика, брошенного горизонтально.
1. Соберите экспериментальную установку (см. рис. 345), устанавливая высоту вылета шарика $h = 196 \text{ мм}$ (для упрощения расчётов). При измерении $\text{h}$ линейкой с миллиметровыми делениями можно принять, что максимальная абсолютная погрешность $\Delta h = 1 \text{ мм}$, т. е.
$h = (196 \pm 1) \text{ мм}$.
Решение. №1 (с. 440)
Способ измерения начальной скорости шарика, брошенного горизонтально, основывается на принципе независимости движений. Движение шарика рассматривается как результат сложения двух независимых движений: равномерного прямолинейного движения в горизонтальном направлении и равноускоренного движения (свободного падения) в вертикальном направлении.
Для определения начальной скорости необходимо выполнить следующие шаги:
1. Собрать экспериментальную установку, например, используя наклонный желоб, установленный на краю стола, так, чтобы шарик в момент отрыва двигался строго горизонтально. Установить и измерить с помощью линейки высоту вылета шарика $h$ от точки старта до поверхности, на которую он будет падать. Согласно заданию, для упрощения расчетов эта высота принимается равной $h = 196$ мм. Принимая во внимание, что измерение производится линейкой с миллиметровыми делениями, максимальная абсолютная погрешность $\Delta h = 1$ мм, то есть $h = (196 \pm 1)$ мм.
2. Определить и отметить на полу точку, находящуюся строго под точкой вылета шарика. Это можно сделать с помощью отвеса. Эта точка будет служить началом отсчета для измерения дальности полета. В предполагаемое место падения шарика следует положить лист белой бумаги, а на него — лист копировальной бумаги. Это позволит точно зафиксировать точку приземления шарика.
3. Произвести запуск шарика. Важно запускать его каждый раз с одной и той же высоты на наклонном желобе, чтобы начальная скорость была одинаковой. После падения шарика на бумаге останется четкий след. Измерить с помощью линейки или рулетки дальность полета $L$ — расстояние по горизонтали от начальной точки отсчета до следа от падения шарика.
4. Для уменьшения влияния случайных погрешностей и получения более точного результата эксперимент следует повторить несколько раз (например, 3-5 раз). Каждый раз измеряя дальность полета $L_i$, а затем рассчитать среднее значение дальности полета $\bar{L}$.
5. Используя измеренные значения, рассчитать начальную скорость шарика $v_0$ по расчетной формуле, вывод которой представлен ниже.
Дано:
Высота вылета шарика $h = (196 \pm 1)$ мм.
Ускорение свободного падения $g \approx 9.8$ м/с2.
Перевод в систему СИ:
$h = (0.196 \pm 0.001)$ м.
Найти:
Начальную скорость шарика $v_0$.
Решение:
Рассмотрим движение шарика по двум осям. Ось OX направим горизонтально в сторону полета, а ось OY — вертикально вниз. Начало координат поместим в точку вылета шарика.
Движение по горизонтали (ось OX) является равномерным, так как сила тяжести действует вертикально и не влияет на горизонтальную составляющую скорости. Уравнение движения:
$x(t) = v_0 t$
Движение по вертикали (ось OY) является равноускоренным (свободное падение), так как начальная вертикальная скорость равна нулю. Уравнение движения:
$y(t) = \frac{gt^2}{2}$
В момент падения шарик преодолеет по вертикали расстояние $h$, а по горизонтали — расстояние $L$ (дальность полета). Время полета $t_{пол}$ можно найти из уравнения для вертикального движения, подставив $y(t_{пол}) = h$:
$h = \frac{gt_{пол}^2}{2}$
Выразим отсюда время полета:
$t_{пол} = \sqrt{\frac{2h}{g}}$
За это же время шарик пролетит по горизонтали расстояние $L$. Подставим время полета в уравнение для горизонтального движения $L = x(t_{пол})$:
$L = v_0 t_{пол} = v_0 \sqrt{\frac{2h}{g}}$
Из этого соотношения выразим искомую начальную скорость $v_0$:
$v_0 = \frac{L}{\sqrt{\frac{2h}{g}}} = L \sqrt{\frac{g}{2h}}$
Это и есть расчетная формула. Для вычисления $v_0$ необходимо экспериментально измерить дальность полета $L$.
Вычислим время полета для заданной высоты, чтобы продемонстрировать упрощение расчетов:
$t_{пол} = \sqrt{\frac{2 \cdot 0.196 \, м}{9.8 \, м/с^2}} = \sqrt{\frac{0.392}{9.8} \, с^2} = \sqrt{0.04 \, с^2} = 0.2 \, с$
Тогда формула для расчета начальной скорости для данной установки принимает вид:
$v_0 = \frac{L}{0.2 \, с} = 5L$
Таким образом, измерив дальность полета $L$ в метрах и умножив ее на 5, можно найти начальную скорость $v_0$ в м/с.
Ответ: Способ измерения начальной скорости шарика заключается в следующем: необходимо измерить высоту вылета шарика $h$ и горизонтальную дальность его полета $L$. Начальная скорость рассчитывается по формуле $v_0 = L \sqrt{\frac{g}{2h}}$. При заданной высоте $h = 196$ мм, время полета составляет $t \approx 0.2$ с, и для нахождения начальной скорости (в м/с) достаточно измерить дальность полета $L$ (в м) и умножить это значение на 5.
Другие задания:
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