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Номер 4, страница 77 - гдз по физике 9 класс учебник Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю.
Тип: Учебник
Серия: алгоритм успеха
Издательство: Вентана-граф
Год издания: 2012 - 2026
Цвет обложки: синий изображено здание и радуга
ISBN: 978-5-360-07412-0
Популярные ГДЗ в 9 классе
Глава 2. Динамика. Параграф 12. Инерциальная система отсчёта. Первый закон Ньютона. Сила. Упражнения - номер 4, страница 77.
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" => 1438146 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-4" "field_display_title" => "4" "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 {#1076 #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" => 1437905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #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" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "70" "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 {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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" => 1202 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "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 {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …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" => 1202 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "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 {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …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 {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1437905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "70" "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 {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073} ] #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 {#1113 #items: array:3 [ 0 => App\Models\Branch {#1123 #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" => 1437905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127 #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:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "70" "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 {#1160 #items: array:1 [ 0 => App\Models\Book {#1126 #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" => 1202 "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 {#1128 #items: array:1 [ 0 => App\Models\Term {#1125 #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 {#1129 #items: array:1 [ 0 => App\Models\Term {#1130 #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 {#1131 #items: array:1 [ 0 => App\Models\Term {#1132 #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" => 5174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вентана-граф" "field_cases" => null "field_translit" => "ventana-graf" ] #original: array:6 [ "id" => 5174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вентана-граф" "field_cases" => null "field_translit" => "ventana-graf" ] #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 {#1133 #items: array:3 [ 0 => App\Models\Term {#1134 #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" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "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 {#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:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "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" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "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" => "Александрович" "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 => "*" ] } 2 => App\Models\Term {#1136 #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" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "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 {#1137 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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: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 {#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: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 {#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" => 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 {#1144 #items: array:1 [ 0 => App\Models\Term {#1145 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "алгоритм успеха" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "algoritm uspekha" ] #original: array:8 [ "id" => 4697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "алгоритм успеха" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "algoritm uspekha" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => 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: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" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Term {#1151 #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" => 6900 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "доработанное" "field_cases" => array:6 [ …6] "field_translit" => "dorabotannoe" ] #original: array:6 [ "id" => 6900 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "доработанное" "field_cases" => array:6 [ …6] "field_translit" => "dorabotannoe" ] #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 {#1152 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1156 #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: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" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1202 "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 {#1128} "field_class" => Illuminate\Database\Eloquent\Collection {#1129} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1131} "field_author" => Illuminate\Database\Eloquent\Collection {#1133} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1137} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1138} "field_country" => Illuminate\Database\Eloquent\Collection {#1140} "field_city" => Illuminate\Database\Eloquent\Collection {#1142} "field_series" => Illuminate\Database\Eloquent\Collection {#1144} "field_umk" => Illuminate\Database\Eloquent\Collection {#1146} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1147} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1148} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1150} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1152} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1153} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1154} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1155} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1156} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #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 {#1158 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1437905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127} "field_page_start" => "70" "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 {#1160} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158} ] #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 {#1159 #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" => 1437906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Инерциальная система отсчёта. Первый закон Ньютона. Сила" "field_branch_order" => "12" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ 0 => 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: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" => "71" "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 {#1163 #items: array:1 [ 0 => App\Models\Book {#1126} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1437906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Инерциальная система отсчёта. Первый закон Ньютона. Сила" "field_branch_order" => "12" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1164} "field_page_start" => "71" "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 {#1163} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1162} ] #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 {#1165 #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" => 1437908 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1166 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "77" "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 {#1167 #items: array:1 [ 0 => App\Models\Book {#1126} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1176 #items: array:1 [ 0 => App\Models\Branch {#1175 #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" => 1437906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Инерциальная система отсчёта. Первый закон Ньютона. Сила" "field_branch_order" => "12" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_page_start" => "71" "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 {#1178 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1179 …2} ] #original: array:24 [ "id" => 1437906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Инерциальная система отсчёта. Первый закон Ньютона. Сила" "field_branch_order" => "12" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_page_start" => "71" "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 {#1178 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1179 …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" => 1437908 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1166} "field_page_start" => "77" "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 {#1167} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1176} ] #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 {#1074 #items: array:2 [ 0 => App\Models\Element {#1105 #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" => 1705026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1103 #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" => 6112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …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 {#1102 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …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 {#1102 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 …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" => "1438146" "type" => "task" ] "text" => "<p><strong>4.</strong> Постройте в тетради векторы сил, если известны их проекции на координатные оси X и Y, соответственно: $2 \text{ Н}$ и $5 \text{ Н}$ $3 \text{ Н};$ и $-2 \text{ Н};$ $-1 \text{ Н}$ и $-7 \text{ Н}.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "483" "height" => 102 "path" => "/media/fizika_09/grachev-u/0-12upr/4-1.webp?ts=1759503109" ] ] ] #original: array:7 [ "id" => 1705026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "1438146" "type" => "task" ] "text" => "<p><strong>4.</strong> Постройте в тетради векторы сил, если известны их проекции на координатные оси X и Y, соответственно: $2 \text{ Н}$ и $5 \text{ Н}$ $3 \text{ Н};$ и $-2 \text{ Н};$ $-1 \text{ Н}$ и $-7 \text{ Н}.$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "483" "height" => 102 "path" => "/media/fizika_09/grachev-u/0-12upr/4-1.webp?ts=1759503109" ] ] ] #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 {#1097 #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" => 1812710 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Edition {#1098 #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" => 6644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …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 {#1094 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …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 {#1094 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …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" => "1438146" "type" => "task" ] "text" => "<p>Для построения векторов сил в декартовой системе координат $XOY$ необходимо выбрать масштаб. Например, пусть одна клетка тетради (или 1 см) соответствует 1 Н. Начало каждого вектора следует поместить в начало координат — точку $O(0,0)$. Конец вектора будет находиться в точке, координаты которой равны проекциям этого вектора на оси $\text{X}$ и $\text{Y}$.</p><p><strong>2 </strong>Н и 5 Н</p><p>Обозначим этот вектор силы как $\vec{F_1}$. Его проекции на оси координат равны $F_{1x} = 2$ Н и $F_{1y} = 5$ Н. Для построения этого вектора нужно отложить от начала координат 2 единицы в положительном направлении оси $\text{X}$ и 5 единиц в положительном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(2, 5)$. Вектор $\vec{F_1}$ — это направленный отрезок, проведенный из начала координат в эту точку.</p><p>Модуль (длина) вектора силы вычисляется по теореме Пифагора:</p><p>$|\vec{F_1}| = \sqrt{F_{1x}^2 + F_{1y}^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39$ Н.</p><p><strong>Ответ:</strong> Вектор строится из начала координат в точку с координатами (2, 5). Его модуль равен $\sqrt{29}$ Н.</p><p><strong>3 </strong>Н и -2 Н</p><p>Обозначим этот вектор силы как $\vec{F_2}$. Его проекции: $F_{2x} = 3$ Н и $F_{2y} = -2$ Н. Для построения этого вектора откладываем от начала координат 3 единицы в положительном направлении оси $\text{X}$ и 2 единицы в отрицательном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(3, -2)$. Вектор $\vec{F_2}$ — это направленный отрезок из начала координат в эту точку.</p><p>Модуль этого вектора:</p><p>$|\vec{F_2}| = \sqrt{F_{2x}^2 + F_{2y}^2} = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.61$ Н.</p><p><strong>Ответ:</strong> Вектор строится из начала координат в точку с координатами (3, -2). Его модуль равен $\sqrt{13}$ Н.</p><p><strong>-1 Н и -7 Н</strong></p><p>Обозначим этот вектор силы как $\vec{F_3}$. Его проекции: $F_{3x} = -1$ Н и $F_{3y} = -7$ Н. Для построения этого вектора откладываем от начала координат 1 единицу в отрицательном направлении оси $\text{X}$ и 7 единиц в отрицательном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(-1, -7)$. Вектор $\vec{F_3}$ — это направленный отрезок из начала координат в эту точку.</p><p>Модуль этого вектора:</p><p>$|\vec{F_3}| = \sqrt{F_{3x}^2 + F_{3y}^2} = \sqrt{(-1)^2 + (-7)^2} = \sqrt{1 + 49} = \sqrt{50} = 5\sqrt{2} \approx 7.07$ Н.</p><p><strong>Ответ:</strong> Вектор строится из начала координат в точку с координатами (-1, -7). Его модуль равен $\sqrt{50}$ Н.</p><p>Общее графическое построение всех трех векторов в одной системе координат:</p><svg width="300" height="400" viewBox="-50 -90 100 180" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_red" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="red"></path></marker><marker id="arrow_blue" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="blue"></path></marker><marker id="arrow_green" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="green"></path></marker></defs><!-- Grid and Axes --><path d="M -50 0 L 50 0 M 0 -90 L 0 90" stroke="black" stroke-width="1"></path><path d="M 45 -3 L 50 0 L 45 3" stroke="black" fill="none" stroke-width="1"></path><!-- X-arrow --><path d="M -3 -85 L 0 -90 L 3 -85" stroke="black" fill="none" stroke-width="1"></path><!-- Y-arrow --><g stroke="#cccccc" stroke-width="0.5"><path d="M -50 10 L 50 10 M -50 20 L 50 20 M -50 30 L 50 30 M -50 40 L 50 40 M -50 50 L 50 50 M -50 60 L 50 60 M -50 70 L 50 70 M -50 80 L 50 80 M -50 -10 L 50 -10 M -50 -20 L 50 -20 M -50 -30 L 50 -30 M -50 -40 L 50 -40 M -50 -50 L 50 -50 M -50 -60 L 50 -60 M -50 -70 L 50 -70 M -50 -80 L 50 -80"></path><path d="M 10 -90 L 10 90 M 20 -90 L 20 90 M 30 -90 L 30 90 M 40 -90 L 40 90 M -10 -90 L -10 90 M -20 -90 L -20 90 M -30 -90 L -30 90 M -40 -90 L -40 90"></path></g><!-- Axes Labels --><text x="40" y="-5" font-family="sans-serif" font-size="8" fill="black">X</text><text x="5" y="-80" font-family="sans-serif" font-size="8" fill="black">Y</text><!-- Vectors --><!-- F1: (2, 5) -> (20, -50) --><line x1="0" y1="0" x2="20" y2="-50" stroke="red" stroke-width="1.5" marker-end="url(#arrow_red)"></line><text x="22" y="-52" font-family="sans-serif" font-size="10" fill="red">F₁</text><!-- F2: (3, -2) -> (30, 20) --><line x1="0" y1="0" x2="30" y2="20" stroke="blue" stroke-width="1.5" marker-end="url(#arrow_blue)"></line><text x="32" y="22" font-family="sans-serif" font-size="10" fill="blue">F₂</text><!-- F3: (-1, -7) -> (-10, 70) --><line x1="0" y1="0" x2="-10" y2="70" stroke="green" stroke-width="1.5" marker-end="url(#arrow_green)"></line><text x="-18" y="75" font-family="sans-serif" font-size="10" fill="green">F₃</text></svg>" ] #original: array:6 [ "id" => 1812710 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1089} "task" => array:2 [ "refs" => "1438146" "type" => "task" ] "text" => "<p>Для построения векторов сил в декартовой системе координат $XOY$ необходимо выбрать масштаб. Например, пусть одна клетка тетради (или 1 см) соответствует 1 Н. Начало каждого вектора следует поместить в начало координат — точку $O(0,0)$. Конец вектора будет находиться в точке, координаты которой равны проекциям этого вектора на оси $\text{X}$ и $\text{Y}$.</p><p><strong>2 </strong>Н и 5 Н</p><p>Обозначим этот вектор силы как $\vec{F_1}$. Его проекции на оси координат равны $F_{1x} = 2$ Н и $F_{1y} = 5$ Н. Для построения этого вектора нужно отложить от начала координат 2 единицы в положительном направлении оси $\text{X}$ и 5 единиц в положительном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(2, 5)$. Вектор $\vec{F_1}$ — это направленный отрезок, проведенный из начала координат в эту точку.</p><p>Модуль (длина) вектора силы вычисляется по теореме Пифагора:</p><p>$|\vec{F_1}| = \sqrt{F_{1x}^2 + F_{1y}^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39$ Н.</p><p><strong>Ответ:</strong> Вектор строится из начала координат в точку с координатами (2, 5). Его модуль равен $\sqrt{29}$ Н.</p><p><strong>3 </strong>Н и -2 Н</p><p>Обозначим этот вектор силы как $\vec{F_2}$. Его проекции: $F_{2x} = 3$ Н и $F_{2y} = -2$ Н. Для построения этого вектора откладываем от начала координат 3 единицы в положительном направлении оси $\text{X}$ и 2 единицы в отрицательном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(3, -2)$. Вектор $\vec{F_2}$ — это направленный отрезок из начала координат в эту точку.</p><p>Модуль этого вектора:</p><p>$|\vec{F_2}| = \sqrt{F_{2x}^2 + F_{2y}^2} = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.61$ Н.</p><p><strong>Ответ:</strong> Вектор строится из начала координат в точку с координатами (3, -2). Его модуль равен $\sqrt{13}$ Н.</p><p><strong>-1 Н и -7 Н</strong></p><p>Обозначим этот вектор силы как $\vec{F_3}$. Его проекции: $F_{3x} = -1$ Н и $F_{3y} = -7$ Н. Для построения этого вектора откладываем от начала координат 1 единицу в отрицательном направлении оси $\text{X}$ и 7 единиц в отрицательном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(-1, -7)$. Вектор $\vec{F_3}$ — это направленный отрезок из начала координат в эту точку.</p><p>Модуль этого вектора:</p><p>$|\vec{F_3}| = \sqrt{F_{3x}^2 + F_{3y}^2} = \sqrt{(-1)^2 + (-7)^2} = \sqrt{1 + 49} = \sqrt{50} = 5\sqrt{2} \approx 7.07$ Н.</p><p><strong>Ответ:</strong> Вектор строится из начала координат в точку с координатами (-1, -7). Его модуль равен $\sqrt{50}$ Н.</p><p>Общее графическое построение всех трех векторов в одной системе координат:</p><svg width="300" height="400" viewBox="-50 -90 100 180" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_red" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="red"></path></marker><marker id="arrow_blue" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="blue"></path></marker><marker id="arrow_green" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="green"></path></marker></defs><!-- Grid and Axes --><path d="M -50 0 L 50 0 M 0 -90 L 0 90" stroke="black" stroke-width="1"></path><path d="M 45 -3 L 50 0 L 45 3" stroke="black" fill="none" stroke-width="1"></path><!-- X-arrow --><path d="M -3 -85 L 0 -90 L 3 -85" stroke="black" fill="none" stroke-width="1"></path><!-- Y-arrow --><g stroke="#cccccc" stroke-width="0.5"><path d="M -50 10 L 50 10 M -50 20 L 50 20 M -50 30 L 50 30 M -50 40 L 50 40 M -50 50 L 50 50 M -50 60 L 50 60 M -50 70 L 50 70 M -50 80 L 50 80 M -50 -10 L 50 -10 M -50 -20 L 50 -20 M -50 -30 L 50 -30 M -50 -40 L 50 -40 M -50 -50 L 50 -50 M -50 -60 L 50 -60 M -50 -70 L 50 -70 M -50 -80 L 50 -80"></path><path d="M 10 -90 L 10 90 M 20 -90 L 20 90 M 30 -90 L 30 90 M 40 -90 L 40 90 M -10 -90 L -10 90 M -20 -90 L -20 90 M -30 -90 L -30 90 M -40 -90 L -40 90"></path></g><!-- Axes Labels --><text x="40" y="-5" font-family="sans-serif" font-size="8" fill="black">X</text><text x="5" y="-80" font-family="sans-serif" font-size="8" fill="black">Y</text><!-- Vectors --><!-- F1: (2, 5) -> (20, -50) --><line x1="0" y1="0" x2="20" y2="-50" stroke="red" stroke-width="1.5" marker-end="url(#arrow_red)"></line><text x="22" y="-52" font-family="sans-serif" font-size="10" fill="red">F₁</text><!-- F2: (3, -2) -> (30, 20) --><line x1="0" y1="0" x2="30" y2="20" stroke="blue" stroke-width="1.5" marker-end="url(#arrow_blue)"></line><text x="32" y="22" font-family="sans-serif" font-size="10" fill="blue">F₂</text><!-- F3: (-1, -7) -> (-10, 70) --><line x1="0" y1="0" x2="-10" y2="70" stroke="green" stroke-width="1.5" marker-end="url(#arrow_green)"></line><text x="-18" y="75" font-family="sans-serif" font-size="10" fill="green">F₃</text></svg>" ] #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" => "1438147" "type" => "task" ] "previous" => array:2 [ "refs" => "1438145" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1126} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\BookPage {#1110 #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" => 1437583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_url" => "/9-klass/fizika/grachev-uchebnik/page-77" "field_display_title" => "77" "field_folder" => "1" "field_image_name" => "77" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Book {#1126} ] #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 {#1088 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Element {#1075 #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" => 1705579 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1705579 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112 …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" => "1437584" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1437582" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:6 [ 0 => App\Models\Task {#1286 #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" => 1438143 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1287 …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 {#1288 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 …2} "content" => Illuminate\Database\Eloquent\Collection {#1292 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1298 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438143 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1287 …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 {#1288 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 …2} "content" => Illuminate\Database\Eloquent\Collection {#1292 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1298 …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 {#1293 #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" => 1438144 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1291 …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 {#1300 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1294 …2} "content" => Illuminate\Database\Eloquent\Collection {#1295 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1310 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438144 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1291 …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 {#1300 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1294 …2} "content" => Illuminate\Database\Eloquent\Collection {#1295 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1310 …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 {#1305 #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" => 1438145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1297 …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 {#1312 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1308 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1307 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1322 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1297 …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 {#1312 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1308 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1307 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1322 …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 {#1317 #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" => 1438146 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1309 …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 {#1324 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1320 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1318 …2} "content" => Illuminate\Database\Eloquent\Collection {#1321 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1319 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438146 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1309 …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 {#1324 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1320 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1318 …2} "content" => Illuminate\Database\Eloquent\Collection {#1321 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1319 …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 => "*" ] } 4 => App\Models\Task {#1329 #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" => 1438147 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1330 …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 {#1331 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1332 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1333 …2} "content" => Illuminate\Database\Eloquent\Collection {#1335 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1341 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438147 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1330 …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 {#1331 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1332 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1333 …2} "content" => Illuminate\Database\Eloquent\Collection {#1335 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1341 …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 => "*" ] } 5 => App\Models\Task {#1336 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1438148 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1334 …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 {#1343 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1339 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1337 …2} …5 ] #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" => 1437583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_url" => "/9-klass/fizika/grachev-uchebnik/page-77" "field_display_title" => "77" "field_folder" => "1" "field_image_name" => "77" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1090} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1086} "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 {#1088} "content" => Illuminate\Database\Eloquent\Collection {#1114} "next" => array:2 [ "refs" => "1437584" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1437582" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1274} ] #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" => 1438146 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "77" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/12upr-4" "field_display_title" => "4" "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 {#1076} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1113} "content" => Illuminate\Database\Eloquent\Collection {#1074} "next" => array:2 [ "refs" => "1438147" "type" => "task" ] "previous" => array:2 [ "refs" => "1438145" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1108} "page" => array:2 [ "refs" => "1437583" "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 => "*" ] }
№4 (с. 77)
Условие. №4 (с. 77)
скриншот условия
4. Постройте в тетради векторы сил, если известны их проекции на координатные оси X и Y, соответственно: $2 \text{ Н}$ и $5 \text{ Н}$ $3 \text{ Н};$ и $-2 \text{ Н};$ $-1 \text{ Н}$ и $-7 \text{ Н}.$
Решение. №4 (с. 77)
Для построения векторов сил в декартовой системе координат $XOY$ необходимо выбрать масштаб. Например, пусть одна клетка тетради (или 1 см) соответствует 1 Н. Начало каждого вектора следует поместить в начало координат — точку $O(0,0)$. Конец вектора будет находиться в точке, координаты которой равны проекциям этого вектора на оси $\text{X}$ и $\text{Y}$.
2 Н и 5 Н
Обозначим этот вектор силы как $\vec{F_1}$. Его проекции на оси координат равны $F_{1x} = 2$ Н и $F_{1y} = 5$ Н. Для построения этого вектора нужно отложить от начала координат 2 единицы в положительном направлении оси $\text{X}$ и 5 единиц в положительном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(2, 5)$. Вектор $\vec{F_1}$ — это направленный отрезок, проведенный из начала координат в эту точку.
Модуль (длина) вектора силы вычисляется по теореме Пифагора:
$|\vec{F_1}| = \sqrt{F_{1x}^2 + F_{1y}^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39$ Н.
Ответ: Вектор строится из начала координат в точку с координатами (2, 5). Его модуль равен $\sqrt{29}$ Н.
3 Н и -2 Н
Обозначим этот вектор силы как $\vec{F_2}$. Его проекции: $F_{2x} = 3$ Н и $F_{2y} = -2$ Н. Для построения этого вектора откладываем от начала координат 3 единицы в положительном направлении оси $\text{X}$ и 2 единицы в отрицательном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(3, -2)$. Вектор $\vec{F_2}$ — это направленный отрезок из начала координат в эту точку.
Модуль этого вектора:
$|\vec{F_2}| = \sqrt{F_{2x}^2 + F_{2y}^2} = \sqrt{3^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.61$ Н.
Ответ: Вектор строится из начала координат в точку с координатами (3, -2). Его модуль равен $\sqrt{13}$ Н.
-1 Н и -7 Н
Обозначим этот вектор силы как $\vec{F_3}$. Его проекции: $F_{3x} = -1$ Н и $F_{3y} = -7$ Н. Для построения этого вектора откладываем от начала координат 1 единицу в отрицательном направлении оси $\text{X}$ и 7 единиц в отрицательном направлении оси $\text{Y}$. Конечная точка вектора будет иметь координаты $(-1, -7)$. Вектор $\vec{F_3}$ — это направленный отрезок из начала координат в эту точку.
Модуль этого вектора:
$|\vec{F_3}| = \sqrt{F_{3x}^2 + F_{3y}^2} = \sqrt{(-1)^2 + (-7)^2} = \sqrt{1 + 49} = \sqrt{50} = 5\sqrt{2} \approx 7.07$ Н.
Ответ: Вектор строится из начала координат в точку с координатами (-1, -7). Его модуль равен $\sqrt{50}$ Н.
Общее графическое построение всех трех векторов в одной системе координат:
Другие задания:
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