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Номер 2, страница 33 - 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
Механика. 2. Кинематика материальной точки. Параграф 9. Скорость. Задачи - номер 2, страница 33.
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" => 1389717 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09zad-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" => 1389404 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "18" "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" => 1389404 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "18" "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 {#1108 #items: array:4 [ 0 => App\Models\Branch {#1118 #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" => 1389404 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "18" "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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1120 #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 {#1122 #items: array:1 [ 0 => App\Models\Term {#1121 #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 {#1123 #items: array:1 [ 0 => App\Models\Term {#1124 #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 {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #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 {#1127 #items: array:1 [ 0 => App\Models\Term {#1128 #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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #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 {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #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 {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #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 {#1136 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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 {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #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)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => 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_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #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" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #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_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144 #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 {#1145 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1149 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ …6] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ …6] "field_translit" => "belyy" ] #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 "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 {#1122} "field_class" => Illuminate\Database\Eloquent\Collection {#1123} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125} "field_author" => Illuminate\Database\Eloquent\Collection {#1127} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_country" => Illuminate\Database\Eloquent\Collection {#1132} "field_city" => Illuminate\Database\Eloquent\Collection {#1134} "field_series" => Illuminate\Database\Eloquent\Collection {#1136} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144} "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 {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389404 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119} "field_page_start" => "18" "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150} ] #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 {#1151 #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" => 1389405 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Кинематика материальной точки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "18" "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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389405 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Кинематика материальной точки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_page_start" => "18" "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 {#1154} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155} ] #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 {#1156 #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" => 1389408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Скорость" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Term {#1157 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "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_page_start" => "27" "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 {#1159 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:1 [ 0 => App\Models\Branch {#1167 #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" => 1389405 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Кинематика материальной точки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_page_start" => "18" "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 {#1170 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171 …2} ] #original: array:24 [ "id" => 1389405 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Кинематика материальной точки" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_page_start" => "18" "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 {#1170 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171 …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" => 1389408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Скорость" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1160} "field_page_start" => "27" "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 {#1159} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1168} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Branch {#1161 #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" => 1389410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "33" "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 {#1164 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Branch {#1176 #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" => 1389408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Скорость" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_page_start" => "27" "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 {#1179 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1180 …2} ] #original: array:24 [ "id" => 1389408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Скорость" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_page_start" => "27" "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 {#1179 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1180 …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" => 1389410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1158} "field_page_start" => "33" "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 {#1164} "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 {#1071 #items: array:2 [ 0 => App\Models\Element {#1099 #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" => 1640025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Edition {#1097 #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 {#1095 …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 {#1096 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …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 {#1095 …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 {#1096 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …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" => "1389717" "type" => "task" ] "text" => "<p><strong>2.</strong> Самолёт пролетел первую треть пути со скоростью 1100 км/ч, а оставшийся путь со скоростью 800 км/ч. Найдите среднюю скорость его полёта.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1701" "height" => 183 "path" => "/media/fizika_10/kasyanov-u/0-09zad/2-1.webp?ts=1757952701" ] ] ] #original: array:7 [ "id" => 1640025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089} "task" => array:2 [ "refs" => "1389717" "type" => "task" ] "text" => "<p><strong>2.</strong> Самолёт пролетел первую треть пути со скоростью 1100 км/ч, а оставшийся путь со скоростью 800 км/ч. Найдите среднюю скорость его полёта.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1701" "height" => 183 "path" => "/media/fizika_10/kasyanov-u/0-09zad/2-1.webp?ts=1757952701" ] ] ] #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 {#1092 #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" => 1692729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Edition {#1091 #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 {#1087 …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 {#1088 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …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 {#1087 …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 {#1088 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …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" => "1389717" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Скорость на первом участке пути, $v_1 = 1100$ км/ч.</p><p>Длина первого участка пути, $S_1 = \frac{1}{3}S$, где $S$ - весь путь.</p><p>Скорость на втором участке пути, $v_2 = 800$ км/ч.</p><p>Длина второго участка пути, $S_2 = S - S_1 = \frac{2}{3}S$.</p><p>Расчеты будут проводиться в км/ч, так как все данные приведены в согласованных единицах.</p><p><strong>Найти:</strong></p><p>Среднюю скорость полета $v_{ср}$.</p><p><strong>Решение:</strong></p><p>Средняя скорость движения определяется как отношение всего пройденного пути ко всему затраченному времени. Формула для средней скорости:</p><p>$v_{ср} = \frac{S_{общ}}{t_{общ}}$</p><p>Весь пройденный путь $S_{общ}$ равен $S$.</p><p>Общее время движения $t_{общ}$ равно сумме времени, затраченного на каждый участок:</p><p>$t_{общ} = t_1 + t_2$</p><p>Время, затраченное на прохождение первого участка пути:</p><p>$t_1 = \frac{S_1}{v_1} = \frac{\frac{1}{3}S}{v_1} = \frac{S}{3v_1}$</p><p>Время, затраченное на прохождение второго, оставшегося, участка пути:</p><p>$t_2 = \frac{S_2}{v_2} = \frac{\frac{2}{3}S}{v_2} = \frac{2S}{3v_2}$</p><p>Теперь найдем общее время движения, сложив время на каждом из участков:</p><p>$t_{общ} = t_1 + t_2 = \frac{S}{3v_1} + \frac{2S}{3v_2} = S \left( \frac{1}{3v_1} + \frac{2}{3v_2} \right)$</p><p>Приведем дроби в скобках к общему знаменателю:</p><p>$t_{общ} = S \left( \frac{v_2 + 2v_1}{3v_1v_2} \right)$</p><p>Теперь подставим выражения для общего пути и общего времени в формулу для средней скорости:</p><p>$v_{ср} = \frac{S}{S \left( \frac{v_2 + 2v_1}{3v_1v_2} \right)}$</p><p>Сократив $S$, получим итоговую формулу для расчета средней скорости:</p><p>$v_{ср} = \frac{1}{\frac{v_2 + 2v_1}{3v_1v_2}} = \frac{3v_1v_2}{2v_1 + v_2}$</p><p>Подставим числовые значения из условия задачи в полученную формулу:</p><p>$v_{ср} = \frac{3 \cdot 1100 \cdot 800}{2 \cdot 1100 + 800} = \frac{2640000}{2200 + 800} = \frac{2640000}{3000} = 880$ км/ч.</p><p><strong>Ответ:</strong> средняя скорость полета самолёта составляет 880 км/ч.</p>" ] #original: array:6 [ "id" => 1692729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1389717" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Скорость на первом участке пути, $v_1 = 1100$ км/ч.</p><p>Длина первого участка пути, $S_1 = \frac{1}{3}S$, где $S$ - весь путь.</p><p>Скорость на втором участке пути, $v_2 = 800$ км/ч.</p><p>Длина второго участка пути, $S_2 = S - S_1 = \frac{2}{3}S$.</p><p>Расчеты будут проводиться в км/ч, так как все данные приведены в согласованных единицах.</p><p><strong>Найти:</strong></p><p>Среднюю скорость полета $v_{ср}$.</p><p><strong>Решение:</strong></p><p>Средняя скорость движения определяется как отношение всего пройденного пути ко всему затраченному времени. Формула для средней скорости:</p><p>$v_{ср} = \frac{S_{общ}}{t_{общ}}$</p><p>Весь пройденный путь $S_{общ}$ равен $S$.</p><p>Общее время движения $t_{общ}$ равно сумме времени, затраченного на каждый участок:</p><p>$t_{общ} = t_1 + t_2$</p><p>Время, затраченное на прохождение первого участка пути:</p><p>$t_1 = \frac{S_1}{v_1} = \frac{\frac{1}{3}S}{v_1} = \frac{S}{3v_1}$</p><p>Время, затраченное на прохождение второго, оставшегося, участка пути:</p><p>$t_2 = \frac{S_2}{v_2} = \frac{\frac{2}{3}S}{v_2} = \frac{2S}{3v_2}$</p><p>Теперь найдем общее время движения, сложив время на каждом из участков:</p><p>$t_{общ} = t_1 + t_2 = \frac{S}{3v_1} + \frac{2S}{3v_2} = S \left( \frac{1}{3v_1} + \frac{2}{3v_2} \right)$</p><p>Приведем дроби в скобках к общему знаменателю:</p><p>$t_{общ} = S \left( \frac{v_2 + 2v_1}{3v_1v_2} \right)$</p><p>Теперь подставим выражения для общего пути и общего времени в формулу для средней скорости:</p><p>$v_{ср} = \frac{S}{S \left( \frac{v_2 + 2v_1}{3v_1v_2} \right)}$</p><p>Сократив $S$, получим итоговую формулу для расчета средней скорости:</p><p>$v_{ср} = \frac{1}{\frac{v_2 + 2v_1}{3v_1v_2}} = \frac{3v_1v_2}{2v_1 + v_2}$</p><p>Подставим числовые значения из условия задачи в полученную формулу:</p><p>$v_{ср} = \frac{3 \cdot 1100 \cdot 800}{2 \cdot 1100 + 800} = \frac{2640000}{2200 + 800} = \frac{2640000}{3000} = 880$ км/ч.</p><p><strong>Ответ:</strong> средняя скорость полета самолёта составляет 880 км/ч.</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" => "1389718" "type" => "task" ] "previous" => array:2 [ "refs" => "1389716" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Book {#1120} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\BookPage {#1104 #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" => 1390681 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-33" "field_display_title" => "33" "field_folder" => "1" "field_image_name" => "33" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1120} ] #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 {#1080 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Element {#1114 #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" => 1641181 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1641181 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1390682" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1390680" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:10 [ 0 => App\Models\Task {#1295 #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" => 1389711 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1296 …2} "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 {#1297 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1298 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1476 …2} "content" => Illuminate\Database\Eloquent\Collection {#1401 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1442 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1389711 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1296 …2} "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 {#1297 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1298 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1476 …2} "content" => Illuminate\Database\Eloquent\Collection {#1401 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1442 …2} "page" => array:2 [ …2] ] #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\Task {#1435 #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" => 1389712 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1484 …2} "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 {#1471 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1440 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1436 …2} "content" => Illuminate\Database\Eloquent\Collection {#1439 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1461 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1389712 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1484 …2} "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 {#1471 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1440 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1436 …2} "content" => Illuminate\Database\Eloquent\Collection {#1439 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1461 …2} "page" => array:2 [ …2] ] #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\Task {#1467 #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" => 1389713 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1473 …2} "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 {#1460 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1463 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1465 …2} "content" => Illuminate\Database\Eloquent\Collection {#1466 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1451 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1389713 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1473 …2} "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 {#1460 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1463 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1465 …2} "content" => Illuminate\Database\Eloquent\Collection {#1466 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1451 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1456 #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" => 1389714 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1464 …2} "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 {#1449 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1452 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1453 …2} "content" => Illuminate\Database\Eloquent\Collection {#1454 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1432 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1389714 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09vopr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1464 …2} "field_metatags_title" => null …14 ] #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 {#1441 #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 {#1426 #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 {#1412 #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 {#1333 #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] } 8 => App\Models\Task {#1399 #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] } 9 => App\Models\Task {#1386 #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" => 1390681 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-33" "field_display_title" => "33" "field_folder" => "1" "field_image_name" => "33" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1084} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082} "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 {#1080} "content" => Illuminate\Database\Eloquent\Collection {#1113} "next" => array:2 [ "refs" => "1390682" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1390680" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1279} ] #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" => 1389717 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "33" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/09zad-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 {#1108} "content" => Illuminate\Database\Eloquent\Collection {#1071} "next" => array:2 [ "refs" => "1389718" "type" => "task" ] "previous" => array:2 [ "refs" => "1389716" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102} "page" => array:2 [ "refs" => "1390681" "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. 33)
Условие. №2 (с. 33)
скриншот условия
2. Самолёт пролетел первую треть пути со скоростью 1100 км/ч, а оставшийся путь со скоростью 800 км/ч. Найдите среднюю скорость его полёта.
Решение. №2 (с. 33)
Дано:
Скорость на первом участке пути, $v_1 = 1100$ км/ч.
Длина первого участка пути, $S_1 = \frac{1}{3}S$, где $S$ - весь путь.
Скорость на втором участке пути, $v_2 = 800$ км/ч.
Длина второго участка пути, $S_2 = S - S_1 = \frac{2}{3}S$.
Расчеты будут проводиться в км/ч, так как все данные приведены в согласованных единицах.
Найти:
Среднюю скорость полета $v_{ср}$.
Решение:
Средняя скорость движения определяется как отношение всего пройденного пути ко всему затраченному времени. Формула для средней скорости:
$v_{ср} = \frac{S_{общ}}{t_{общ}}$
Весь пройденный путь $S_{общ}$ равен $S$.
Общее время движения $t_{общ}$ равно сумме времени, затраченного на каждый участок:
$t_{общ} = t_1 + t_2$
Время, затраченное на прохождение первого участка пути:
$t_1 = \frac{S_1}{v_1} = \frac{\frac{1}{3}S}{v_1} = \frac{S}{3v_1}$
Время, затраченное на прохождение второго, оставшегося, участка пути:
$t_2 = \frac{S_2}{v_2} = \frac{\frac{2}{3}S}{v_2} = \frac{2S}{3v_2}$
Теперь найдем общее время движения, сложив время на каждом из участков:
$t_{общ} = t_1 + t_2 = \frac{S}{3v_1} + \frac{2S}{3v_2} = S \left( \frac{1}{3v_1} + \frac{2}{3v_2} \right)$
Приведем дроби в скобках к общему знаменателю:
$t_{общ} = S \left( \frac{v_2 + 2v_1}{3v_1v_2} \right)$
Теперь подставим выражения для общего пути и общего времени в формулу для средней скорости:
$v_{ср} = \frac{S}{S \left( \frac{v_2 + 2v_1}{3v_1v_2} \right)}$
Сократив $S$, получим итоговую формулу для расчета средней скорости:
$v_{ср} = \frac{1}{\frac{v_2 + 2v_1}{3v_1v_2}} = \frac{3v_1v_2}{2v_1 + v_2}$
Подставим числовые значения из условия задачи в полученную формулу:
$v_{ср} = \frac{3 \cdot 1100 \cdot 800}{2 \cdot 1100 + 800} = \frac{2640000}{2200 + 800} = \frac{2640000}{3000} = 880$ км/ч.
Ответ: средняя скорость полета самолёта составляет 880 км/ч.
Другие задания:
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