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Номер 33, страница 8 - гдз по физике 7-9 класс сборник задач Московкина, Волков
Авторы: Московкина Е. Г., Волков В. А.
Тип: Сборник задач
Издательство: ВАКО
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-408-00459-1
Популярные ГДЗ в 7 классе
7 класс. Равномерное прямолинейное движение - номер 33, страница 8.
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" => 1424844 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "8" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-33" "field_display_title" => "33" "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" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "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" => 4994 "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 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1044 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1049 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 #items: 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" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "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} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1039} "field_author" => Illuminate\Database\Eloquent\Collection {#1041} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1044} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1045} "field_country" => Illuminate\Database\Eloquent\Collection {#1047} "field_city" => Illuminate\Database\Eloquent\Collection {#1049} "field_series" => Illuminate\Database\Eloquent\Collection {#1051} "field_umk" => Illuminate\Database\Eloquent\Collection {#1052} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #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" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "4" "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:2 [ 0 => App\Models\Branch {#1023} 1 => 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" => 1424762 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное прямолинейное движение" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "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" => 4994 "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 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "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" => "/7-klass/fizika/moskovkina-sbornik-zadach" "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" => 4994 "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} "field_class" => Illuminate\Database\Eloquent\Collection {#1070} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "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" => "/7-klass/fizika/moskovkina-sbornik-zadach" "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: array:1 [ 0 => 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" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_page_start" => "4" "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 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1131 …2} ] #original: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_page_start" => "4" "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 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1131 …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" => 1424762 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное прямолинейное движение" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_page_start" => "4" "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 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:2 [ 0 => App\Models\Element {#1133 #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" => 1677377 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Edition {#1135 #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" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1138 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1138 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1140 …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" => "1424844" "type" => "task" ] "text" => "<p><strong>33.</strong> Расстояние между городом и дачным поселком $80 \text{ км}$. Из города в направлении поселка выехал автомобиль со скоростью $50 \text{ км/ч}$. Одновременно из поселка в том же направлении, что и автомобиль, выезжает мотоцикл со скоростью $30 \text{ км/ч}$. На каком расстоянии от города автомобиль догонит мотоцикл?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "33-1.jpg" "alt" => null "width" => "2541" "height" => 762 "path" => "/media/fizika_07/moskovkina-sz/0-7/33-1.webp?ts=1758885430" ] ] ] #original: array:7 [ "id" => 1677377 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134} "task" => array:2 [ "refs" => "1424844" "type" => "task" ] "text" => "<p><strong>33.</strong> Расстояние между городом и дачным поселком $80 \text{ км}$. Из города в направлении поселка выехал автомобиль со скоростью $50 \text{ км/ч}$. Одновременно из поселка в том же направлении, что и автомобиль, выезжает мотоцикл со скоростью $30 \text{ км/ч}$. На каком расстоянии от города автомобиль догонит мотоцикл?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "33-1.jpg" "alt" => null "width" => "2541" "height" => 762 "path" => "/media/fizika_07/moskovkina-sz/0-7/33-1.webp?ts=1758885430" ] ] ] #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 {#1141 #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" => 1781225 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Edition {#1143 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1146 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1147 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1146 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1147 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1148 …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" => "1424844" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Начальное расстояние между автомобилем и мотоциклом: $S = 80$ км<br>Скорость автомобиля: $v_а = 50$ км/ч<br>Скорость мотоцикла: $v_м = 30$ км/ч</p><p>$S = 80 \text{ км} = 80 \times 1000 = 80000 \text{ м}$<br>$v_а = 50 \frac{\text{км}}{\text{ч}} = 50 \times \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{125}{9} \text{ м/с} \approx 13,89 \text{ м/с}$<br>$v_м = 30 \frac{\text{км}}{\text{ч}} = 30 \times \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{25}{3} \text{ м/с} \approx 8,33 \text{ м/с}$</p><p><strong>Найти:</strong></p><p>Расстояние от города до места встречи — $S_{в}$</p><p><strong>Решение:</strong></p><p>Это задача на "движение вдогонку". Автомобиль, выехавший из города, догоняет мотоцикл, который стартовал одновременно из дачного поселка в том же направлении. В начальный момент времени расстояние между ними составляло 80 км.</p><p>Поскольку автомобиль движется быстрее мотоцикла, он будет сокращать расстояние между ними. Скорость, с которой автомобиль догоняет мотоцикл, называется скоростью сближения. При движении в одном направлении скорость сближения равна разности скоростей.</p><p>Для удобства вычислений будем использовать исходные единицы измерения (км и км/ч), так как они согласованы.</p><p><strong>1.</strong> Найдем скорость сближения $v_{сбл}$:</p><p>$v_{сбл} = v_а - v_м = 50 \text{ км/ч} - 30 \text{ км/ч} = 20 \text{ км/ч}$</p><p>Это значит, что каждый час расстояние между автомобилем и мотоциклом уменьшается на 20 км.</p><p><strong>2.</strong> Определим время $\text{t}$, через которое автомобиль догонит мотоцикл. Для этого разделим начальное расстояние $\text{S}$ на скорость сближения $v_{сбл}$:</p><p>$t = \frac{S}{v_{сбл}} = \frac{80 \text{ км}}{20 \text{ км/ч}} = 4 \text{ ч}$</p><p>Таким образом, встреча произойдет через 4 часа после начала движения.</p><p><strong>3.</strong> Чтобы найти, на каком расстоянии от города произойдет встреча, нужно вычислить путь, который проехал автомобиль за это время.</p><p>$S_{в} = v_а \cdot t = 50 \text{ км/ч} \cdot 4 \text{ ч} = 200 \text{ км}$</p><p><strong>Ответ:</strong> автомобиль догонит мотоцикл на расстоянии 200 км от города.</p>" ] #original: array:6 [ "id" => 1781225 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142} "task" => array:2 [ "refs" => "1424844" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Начальное расстояние между автомобилем и мотоциклом: $S = 80$ км<br>Скорость автомобиля: $v_а = 50$ км/ч<br>Скорость мотоцикла: $v_м = 30$ км/ч</p><p>$S = 80 \text{ км} = 80 \times 1000 = 80000 \text{ м}$<br>$v_а = 50 \frac{\text{км}}{\text{ч}} = 50 \times \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{125}{9} \text{ м/с} \approx 13,89 \text{ м/с}$<br>$v_м = 30 \frac{\text{км}}{\text{ч}} = 30 \times \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{25}{3} \text{ м/с} \approx 8,33 \text{ м/с}$</p><p><strong>Найти:</strong></p><p>Расстояние от города до места встречи — $S_{в}$</p><p><strong>Решение:</strong></p><p>Это задача на "движение вдогонку". Автомобиль, выехавший из города, догоняет мотоцикл, который стартовал одновременно из дачного поселка в том же направлении. В начальный момент времени расстояние между ними составляло 80 км.</p><p>Поскольку автомобиль движется быстрее мотоцикла, он будет сокращать расстояние между ними. Скорость, с которой автомобиль догоняет мотоцикл, называется скоростью сближения. При движении в одном направлении скорость сближения равна разности скоростей.</p><p>Для удобства вычислений будем использовать исходные единицы измерения (км и км/ч), так как они согласованы.</p><p><strong>1.</strong> Найдем скорость сближения $v_{сбл}$:</p><p>$v_{сбл} = v_а - v_м = 50 \text{ км/ч} - 30 \text{ км/ч} = 20 \text{ км/ч}$</p><p>Это значит, что каждый час расстояние между автомобилем и мотоциклом уменьшается на 20 км.</p><p><strong>2.</strong> Определим время $\text{t}$, через которое автомобиль догонит мотоцикл. Для этого разделим начальное расстояние $\text{S}$ на скорость сближения $v_{сбл}$:</p><p>$t = \frac{S}{v_{сбл}} = \frac{80 \text{ км}}{20 \text{ км/ч}} = 4 \text{ ч}$</p><p>Таким образом, встреча произойдет через 4 часа после начала движения.</p><p><strong>3.</strong> Чтобы найти, на каком расстоянии от города произойдет встреча, нужно вычислить путь, который проехал автомобиль за это время.</p><p>$S_{в} = v_а \cdot t = 50 \text{ км/ч} \cdot 4 \text{ ч} = 200 \text{ км}$</p><p><strong>Ответ:</strong> автомобиль догонит мотоцикл на расстоянии 200 км от города.</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" => "1424845" "type" => "task" ] "previous" => array:2 [ "refs" => "1424843" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1149 #items: array:1 [ 0 => App\Models\Book {#1150 #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" => 4994 "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 {#1151 #items: array:1 [ 0 => App\Models\Term {#1152 #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 {#1153 #items: array:3 [ 0 => App\Models\Term {#1154 #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" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #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\Term {#1155 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #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\Term {#1156 #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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #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 {#1157 #items: array:1 [ 0 => App\Models\Term {#1158 #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" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #original: array:6 [ "id" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #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 {#1159 #items: array:2 [ 0 => App\Models\Term {#1160 #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" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "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 => "*" ] } 1 => App\Models\Term {#1161 #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" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "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 {#1162 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1163 #items: array:1 [ 0 => App\Models\Term {#1164 #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" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "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" => "sbornik zadach" ] #original: array:10 [ "id" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "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" => "sbornik zadach" ] #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 {#1165 #items: array:1 [ 0 => App\Models\Term {#1166 #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 {#1167 #items: array:1 [ 0 => App\Models\Term {#1168 #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 {#1169 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1170 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1171 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1172 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1173 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1174 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1175 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1176 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1177 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1178 #items: array:1 [ 0 => App\Models\Term {#1179 #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" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #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" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "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 {#1151} "field_class" => Illuminate\Database\Eloquent\Collection {#1153} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1157} "field_author" => Illuminate\Database\Eloquent\Collection {#1159} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1162} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1163} "field_country" => Illuminate\Database\Eloquent\Collection {#1165} "field_city" => Illuminate\Database\Eloquent\Collection {#1167} "field_series" => Illuminate\Database\Eloquent\Collection {#1169} "field_umk" => Illuminate\Database\Eloquent\Collection {#1170} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1171} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1172} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1173} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1174} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1175} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1176} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1177} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1178} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #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 {#1499 #items: array:1 [ 0 => App\Models\BookPage {#1184 #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" => 1426111 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "8" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-8" "field_display_title" => "8" "field_folder" => "1" "field_image_name" => "8" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1187 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:1 [ 0 => App\Models\Book {#1188 #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" => 4994 "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 {#1189 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1191 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1195 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1203 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "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 {#1213 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1216 …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" => 4994 "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 {#1189 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1191 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1195 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1203 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "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 {#1213 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1216 …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 } "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 {#1218 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Element {#1220 #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" => 1678643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1221 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1678643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1221 …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" => "1426112" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426110" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:7 [ 0 => App\Models\Task {#1229 #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" => 1424842 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "8" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-31" "field_display_title" => "31" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1230 …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 {#1232 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1233 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1371 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1382 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1424842 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "8" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-31" "field_display_title" => "31" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1230 …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 {#1232 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1233 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1371 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1382 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: 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№33 (с. 8)
Условие. №33 (с. 8)
скриншот условия
33. Расстояние между городом и дачным поселком $80 \text{ км}$. Из города в направлении поселка выехал автомобиль со скоростью $50 \text{ км/ч}$. Одновременно из поселка в том же направлении, что и автомобиль, выезжает мотоцикл со скоростью $30 \text{ км/ч}$. На каком расстоянии от города автомобиль догонит мотоцикл?
Решение. №33 (с. 8)
Дано:
Начальное расстояние между автомобилем и мотоциклом: $S = 80$ км
Скорость автомобиля: $v_а = 50$ км/ч
Скорость мотоцикла: $v_м = 30$ км/ч
$S = 80 \text{ км} = 80 \times 1000 = 80000 \text{ м}$
$v_а = 50 \frac{\text{км}}{\text{ч}} = 50 \times \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{125}{9} \text{ м/с} \approx 13,89 \text{ м/с}$
$v_м = 30 \frac{\text{км}}{\text{ч}} = 30 \times \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{25}{3} \text{ м/с} \approx 8,33 \text{ м/с}$
Найти:
Расстояние от города до места встречи — $S_{в}$
Решение:
Это задача на "движение вдогонку". Автомобиль, выехавший из города, догоняет мотоцикл, который стартовал одновременно из дачного поселка в том же направлении. В начальный момент времени расстояние между ними составляло 80 км.
Поскольку автомобиль движется быстрее мотоцикла, он будет сокращать расстояние между ними. Скорость, с которой автомобиль догоняет мотоцикл, называется скоростью сближения. При движении в одном направлении скорость сближения равна разности скоростей.
Для удобства вычислений будем использовать исходные единицы измерения (км и км/ч), так как они согласованы.
1. Найдем скорость сближения $v_{сбл}$:
$v_{сбл} = v_а - v_м = 50 \text{ км/ч} - 30 \text{ км/ч} = 20 \text{ км/ч}$
Это значит, что каждый час расстояние между автомобилем и мотоциклом уменьшается на 20 км.
2. Определим время $\text{t}$, через которое автомобиль догонит мотоцикл. Для этого разделим начальное расстояние $\text{S}$ на скорость сближения $v_{сбл}$:
$t = \frac{S}{v_{сбл}} = \frac{80 \text{ км}}{20 \text{ км/ч}} = 4 \text{ ч}$
Таким образом, встреча произойдет через 4 часа после начала движения.
3. Чтобы найти, на каком расстоянии от города произойдет встреча, нужно вычислить путь, который проехал автомобиль за это время.
$S_{в} = v_а \cdot t = 50 \text{ км/ч} \cdot 4 \text{ ч} = 200 \text{ км}$
Ответ: автомобиль догонит мотоцикл на расстоянии 200 км от города.
Другие задания:
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