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Номер 2, страница 25, часть 1 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 1
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 1. Глава 1. Кинематика. Параграф 6. Относительность движения. Сложение движений. Принцип независимости движений - номер 2, страница 25.
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" => 1434915 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/06-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #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" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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" => "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 {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 1203 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #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 {#1058 #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 {#1059 #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 => "*" ] } 3 => App\Models\Term {#1060 #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" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "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 {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #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 [ "field_accusative_case" => null "field_creative_case" => null …4 ] "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" => 1203 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "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 {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "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 {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #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 {#1114 #items: array:3 [ 0 => App\Models\Branch {#1124 #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" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1047} ] #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 {#1126 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434806 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "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 {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #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 {#1128 #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" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1129 #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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #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 {#1133 #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" => 1434814 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Относительность движения. Сложение движений. Принцип независимости движений" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 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:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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" => "24" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Branch {#1144 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ …1] #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 {#1147 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146} "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 {#1147} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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" => 1434814 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Относительность движения. Сложение движений. Принцип независимости движений" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "24" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1106 #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" => 1698303 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1104 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100} "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" => "1434915" "type" => "task" ] "text" => "<p><strong>2.</strong> Льдина дрейфует относительно берега моря на восток со скоростью, модуль которой равен 3 м/с (рис. 20). С берегом связана система отсчёта $\text{XY}$, ось $\text{X}$ которой направлена на восток, а ось $\text{Y}$ — на север. Система отсчёта $X'Y'$, оси которой параллельны соответствующим осям системы отсчёта $\text{XY}$, связана со льдиной.</p><p><em>Рис. 20</em></p><p>В системе отсчёта $X'Y'$ (относительно льдины) собака перемещается на запад со скоростью, модуль которой равен 1 м/с, человек толкает сани на восток со скоростью, модуль которой равен 2 м/с, а медведь бежит на север со скоростью, модуль которой равен 4 м/с. Заполните таблицу.</p><p><strong>Объекты</strong></p><p><strong>Величины</strong> | <strong>Льдина</strong> | <strong>Сани</strong> | <strong>Медведь</strong> | <strong>Собака</strong></p><p><strong>Перемещение за 1 с вдоль оси</strong></p><p>$X'$ | | | |</p><p>$Y'$ | | | |</p><p>$\text{X}$ | | | |</p><p>$\text{Y}$ | | | |</p><p><strong>Проекция скорости</strong></p><p>$v_{x'}$ | | | |</p><p>$v_{y'}$ | | | |</p><p>$v_x$ | | | |</p><p>$v_y$ | | | |</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1969" "height" => 2141 "path" => "/media/fizika_09/grachev-rt/0-06/2-1.webp?ts=1759402632" ] ] ] #original: array:7 [ "id" => 1698303 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1434915" "type" => "task" ] "text" => "<p><strong>2.</strong> Льдина дрейфует относительно берега моря на восток со скоростью, модуль которой равен 3 м/с (рис. 20). С берегом связана система отсчёта $\text{XY}$, ось $\text{X}$ которой направлена на восток, а ось $\text{Y}$ — на север. Система отсчёта $X'Y'$, оси которой параллельны соответствующим осям системы отсчёта $\text{XY}$, связана со льдиной.</p><p><em>Рис. 20</em></p><p>В системе отсчёта $X'Y'$ (относительно льдины) собака перемещается на запад со скоростью, модуль которой равен 1 м/с, человек толкает сани на восток со скоростью, модуль которой равен 2 м/с, а медведь бежит на север со скоростью, модуль которой равен 4 м/с. Заполните таблицу.</p><p><strong>Объекты</strong></p><p><strong>Величины</strong> | <strong>Льдина</strong> | <strong>Сани</strong> | <strong>Медведь</strong> | <strong>Собака</strong></p><p><strong>Перемещение за 1 с вдоль оси</strong></p><p>$X'$ | | | |</p><p>$Y'$ | | | |</p><p>$\text{X}$ | | | |</p><p>$\text{Y}$ | | | |</p><p><strong>Проекция скорости</strong></p><p>$v_{x'}$ | | | |</p><p>$v_{y'}$ | | | |</p><p>$v_x$ | | | |</p><p>$v_y$ | | | |</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1969" "height" => 2141 "path" => "/media/fizika_09/grachev-rt/0-06/2-1.webp?ts=1759402632" ] ] ] #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 {#1099 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1734289 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1097 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "1434915" "type" => "task" ] "text" => "<p><strong>Дано</strong></p><p>Скорость льдины относительно берега (система отсчёта XY), $\vec{V}$: модуль $V = 3$ м/с, направление — на восток.</p><p>Скорость собаки относительно льдины (система отсчёта X'Y'), $\vec{v'}_{собака}$: модуль $v'_{собака} = 1$ м/с, направление — на запад.</p><p>Скорость саней относительно льдины, $\vec{v'}_{сани}$: модуль $v'_{сани} = 2$ м/с, направление — на восток.</p><p>Скорость медведя относительно льдины, $\vec{v'}_{медведь}$: модуль $v'_{медведь} = 4$ м/с, направление — на север.</p><p>Промежуток времени, $t = 1$ с.</p><p>Ось X и X' направлены на восток (+).</p><p>Ось Y и Y' направлены на север (+).</p><br><p><strong>Найти</strong></p><p>Для каждого объекта (льдина, сани, медведь, собака) найти:</p><p>1. Перемещение за 1 с вдоль осей X', Y', X, Y: $\Delta x'$, $\Delta y'$, $\Delta x$, $\Delta y$.</p><p>2. Проекции скорости на оси X', Y', X, Y: $v'_{x}$, $v'_{y}$, $v_{x}$, $v_{y}$.</p><br><p><strong>Решение</strong></p><p>В задаче рассматриваются две системы отсчёта:</p><p>1. Неподвижная система отсчёта (НСО) $XY$, связанная с берегом.</p><p>2. Подвижная система отсчёта (ПСО) $X'Y'$, связанная со льдиной. Эта система движется вместе со льдиной на восток со скоростью $\vec{V}$.</p><p>В проекциях на оси скорость ПСО относительно НСО равна: $V_x = 3$ м/с, $V_y = 0$ м/с.</p><p>Для нахождения скорости объекта в неподвижной системе отсчёта ($\vec{v}$) используется закон сложения скоростей: $\vec{v} = \vec{v'} + \vec{V}$, где $\vec{v'}$ — скорость объекта в подвижной системе отсчёта. В проекциях на оси это выглядит так:</p><p>$v_x = v'_x + V_x$</p><p>$v_y = v'_y + V_y$</p><p>Перемещение за время $t$ определяется по формуле $\Delta \vec{r} = \vec{v} \cdot t$. Поскольку $t = 1$ с, то проекции перемещения численно равны проекциям скорости: $\Delta x = v_x \cdot 1 = v_x$, $\Delta y = v_y \cdot 1 = v_y$. Аналогично для ПСО: $\Delta x' = v'_x$, $\Delta y' = v'_y$.</p><p>Рассчитаем искомые величины для каждого объекта.</p><br><p><strong>Льдина</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно самой себя)</i></p><p>Льдина в этой системе неподвижна.</p><p>Проекции скорости: $v'_{x, льдина} = 0$ м/с, $v'_{y, льдина} = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{льдина} = 0$ м, $\Delta y'_{льдина} = 0$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Льдина движется на восток со скоростью 3 м/с. Это и есть скорость подвижной системы отсчёта.</p><p>Проекции скорости: $v_{x, льдина} = V_x = 3$ м/с, $v_{y, льдина} = V_y = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{льдина} = 3 \cdot 1 = 3$ м, $\Delta y_{льдина} = 0 \cdot 1 = 0$ м.</p><p><strong>Ответ:</strong> для льдины: перемещение $\Delta x' = 0$ м, $\Delta y' = 0$ м, $\Delta x = 3$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = 0$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 3$ м/с, $v_{y} = 0$ м/с.</p><br><p><strong>Сани</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно льдины)</i></p><p>Сани движутся на восток (положительное направление оси X') со скоростью 2 м/с.</p><p>Проекции скорости: $v'_{x, сани} = 2$ м/с, $v'_{y, сани} = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{сани} = 2$ м, $\Delta y'_{сани} = 0$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Используем закон сложения скоростей:</p><p>Проекции скорости: $v_{x, сани} = v'_{x, сани} + V_x = 2 + 3 = 5$ м/с. $v_{y, сани} = v'_{y, сани} + V_y = 0 + 0 = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{сани} = 5 \cdot 1 = 5$ м, $\Delta y_{сани} = 0 \cdot 1 = 0$ м.</p><p><strong>Ответ:</strong> для саней: перемещение $\Delta x' = 2$ м, $\Delta y' = 0$ м, $\Delta x = 5$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = 2$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 5$ м/с, $v_{y} = 0$ м/с.</p><br><p><strong>Медведь</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно льдины)</i></p><p>Медведь бежит на север (положительное направление оси Y') со скоростью 4 м/с.</p><p>Проекции скорости: $v'_{x, медведь} = 0$ м/с, $v'_{y, медведь} = 4$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{медведь} = 0$ м, $\Delta y'_{медведь} = 4$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Используем закон сложения скоростей:</p><p>Проекции скорости: $v_{x, медведь} = v'_{x, медведь} + V_x = 0 + 3 = 3$ м/с. $v_{y, медведь} = v'_{y, медведь} + V_y = 4 + 0 = 4$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{медведь} = 3 \cdot 1 = 3$ м, $\Delta y_{медведь} = 4 \cdot 1 = 4$ м.</p><p><strong>Ответ:</strong> для медведя: перемещение $\Delta x' = 0$ м, $\Delta y' = 4$ м, $\Delta x = 3$ м, $\Delta y = 4$ м; проекции скорости $v'_{x} = 0$ м/с, $v'_{y} = 4$ м/с, $v_{x} = 3$ м/с, $v_{y} = 4$ м/с.</p><br><p><strong>Собака</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно льдины)</i></p><p>Собака движется на запад (отрицательное направление оси X') со скоростью 1 м/с.</p><p>Проекции скорости: $v'_{x, собака} = -1$ м/с, $v'_{y, собака} = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{собака} = -1$ м, $\Delta y'_{собака} = 0$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Используем закон сложения скоростей:</p><p>Проекции скорости: $v_{x, собака} = v'_{x, собака} + V_x = -1 + 3 = 2$ м/с. $v_{y, собака} = v'_{y, собака} + V_y = 0 + 0 = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{собака} = 2 \cdot 1 = 2$ м, $\Delta y_{собака} = 0 \cdot 1 = 0$ м.</p><p><strong>Ответ:</strong> для собаки: перемещение $\Delta x' = -1$ м, $\Delta y' = 0$ м, $\Delta x = 2$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = -1$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 2$ м/с, $v_{y} = 0$ м/с.</p>" ] #original: array:6 [ "id" => 1734289 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1434915" "type" => "task" ] "text" => "<p><strong>Дано</strong></p><p>Скорость льдины относительно берега (система отсчёта XY), $\vec{V}$: модуль $V = 3$ м/с, направление — на восток.</p><p>Скорость собаки относительно льдины (система отсчёта X'Y'), $\vec{v'}_{собака}$: модуль $v'_{собака} = 1$ м/с, направление — на запад.</p><p>Скорость саней относительно льдины, $\vec{v'}_{сани}$: модуль $v'_{сани} = 2$ м/с, направление — на восток.</p><p>Скорость медведя относительно льдины, $\vec{v'}_{медведь}$: модуль $v'_{медведь} = 4$ м/с, направление — на север.</p><p>Промежуток времени, $t = 1$ с.</p><p>Ось X и X' направлены на восток (+).</p><p>Ось Y и Y' направлены на север (+).</p><br><p><strong>Найти</strong></p><p>Для каждого объекта (льдина, сани, медведь, собака) найти:</p><p>1. Перемещение за 1 с вдоль осей X', Y', X, Y: $\Delta x'$, $\Delta y'$, $\Delta x$, $\Delta y$.</p><p>2. Проекции скорости на оси X', Y', X, Y: $v'_{x}$, $v'_{y}$, $v_{x}$, $v_{y}$.</p><br><p><strong>Решение</strong></p><p>В задаче рассматриваются две системы отсчёта:</p><p>1. Неподвижная система отсчёта (НСО) $XY$, связанная с берегом.</p><p>2. Подвижная система отсчёта (ПСО) $X'Y'$, связанная со льдиной. Эта система движется вместе со льдиной на восток со скоростью $\vec{V}$.</p><p>В проекциях на оси скорость ПСО относительно НСО равна: $V_x = 3$ м/с, $V_y = 0$ м/с.</p><p>Для нахождения скорости объекта в неподвижной системе отсчёта ($\vec{v}$) используется закон сложения скоростей: $\vec{v} = \vec{v'} + \vec{V}$, где $\vec{v'}$ — скорость объекта в подвижной системе отсчёта. В проекциях на оси это выглядит так:</p><p>$v_x = v'_x + V_x$</p><p>$v_y = v'_y + V_y$</p><p>Перемещение за время $t$ определяется по формуле $\Delta \vec{r} = \vec{v} \cdot t$. Поскольку $t = 1$ с, то проекции перемещения численно равны проекциям скорости: $\Delta x = v_x \cdot 1 = v_x$, $\Delta y = v_y \cdot 1 = v_y$. Аналогично для ПСО: $\Delta x' = v'_x$, $\Delta y' = v'_y$.</p><p>Рассчитаем искомые величины для каждого объекта.</p><br><p><strong>Льдина</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно самой себя)</i></p><p>Льдина в этой системе неподвижна.</p><p>Проекции скорости: $v'_{x, льдина} = 0$ м/с, $v'_{y, льдина} = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{льдина} = 0$ м, $\Delta y'_{льдина} = 0$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Льдина движется на восток со скоростью 3 м/с. Это и есть скорость подвижной системы отсчёта.</p><p>Проекции скорости: $v_{x, льдина} = V_x = 3$ м/с, $v_{y, льдина} = V_y = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{льдина} = 3 \cdot 1 = 3$ м, $\Delta y_{льдина} = 0 \cdot 1 = 0$ м.</p><p><strong>Ответ:</strong> для льдины: перемещение $\Delta x' = 0$ м, $\Delta y' = 0$ м, $\Delta x = 3$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = 0$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 3$ м/с, $v_{y} = 0$ м/с.</p><br><p><strong>Сани</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно льдины)</i></p><p>Сани движутся на восток (положительное направление оси X') со скоростью 2 м/с.</p><p>Проекции скорости: $v'_{x, сани} = 2$ м/с, $v'_{y, сани} = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{сани} = 2$ м, $\Delta y'_{сани} = 0$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Используем закон сложения скоростей:</p><p>Проекции скорости: $v_{x, сани} = v'_{x, сани} + V_x = 2 + 3 = 5$ м/с. $v_{y, сани} = v'_{y, сани} + V_y = 0 + 0 = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{сани} = 5 \cdot 1 = 5$ м, $\Delta y_{сани} = 0 \cdot 1 = 0$ м.</p><p><strong>Ответ:</strong> для саней: перемещение $\Delta x' = 2$ м, $\Delta y' = 0$ м, $\Delta x = 5$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = 2$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 5$ м/с, $v_{y} = 0$ м/с.</p><br><p><strong>Медведь</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно льдины)</i></p><p>Медведь бежит на север (положительное направление оси Y') со скоростью 4 м/с.</p><p>Проекции скорости: $v'_{x, медведь} = 0$ м/с, $v'_{y, медведь} = 4$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{медведь} = 0$ м, $\Delta y'_{медведь} = 4$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Используем закон сложения скоростей:</p><p>Проекции скорости: $v_{x, медведь} = v'_{x, медведь} + V_x = 0 + 3 = 3$ м/с. $v_{y, медведь} = v'_{y, медведь} + V_y = 4 + 0 = 4$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{медведь} = 3 \cdot 1 = 3$ м, $\Delta y_{медведь} = 4 \cdot 1 = 4$ м.</p><p><strong>Ответ:</strong> для медведя: перемещение $\Delta x' = 0$ м, $\Delta y' = 4$ м, $\Delta x = 3$ м, $\Delta y = 4$ м; проекции скорости $v'_{x} = 0$ м/с, $v'_{y} = 4$ м/с, $v_{x} = 3$ м/с, $v_{y} = 4$ м/с.</p><br><p><strong>Собака</strong></p><p>1. <i>В системе отсчёта X'Y' (относительно льдины)</i></p><p>Собака движется на запад (отрицательное направление оси X') со скоростью 1 м/с.</p><p>Проекции скорости: $v'_{x, собака} = -1$ м/с, $v'_{y, собака} = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x'_{собака} = -1$ м, $\Delta y'_{собака} = 0$ м.</p><p>2. <i>В системе отсчёта XY (относительно берега)</i></p><p>Используем закон сложения скоростей:</p><p>Проекции скорости: $v_{x, собака} = v'_{x, собака} + V_x = -1 + 3 = 2$ м/с. $v_{y, собака} = v'_{y, собака} + V_y = 0 + 0 = 0$ м/с.</p><p>Перемещение за 1 с: $\Delta x_{собака} = 2 \cdot 1 = 2$ м, $\Delta y_{собака} = 0 \cdot 1 = 0$ м.</p><p><strong>Ответ:</strong> для собаки: перемещение $\Delta x' = -1$ м, $\Delta y' = 0$ м, $\Delta x = 2$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = -1$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 2$ м/с, $v_{y} = 0$ м/с.</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" => "1434916" "type" => "task" ] "previous" => array:2 [ "refs" => "1434914" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1111 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 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"field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Element {#1118 #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" => 1699047 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1119 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1699047 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1119 …2} "book_page" => array:2 [ …2] "img" => 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#hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1187 #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" => 1435234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/42-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1196 …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 {#1182 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1185 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1154 …2} "content" => Illuminate\Database\Eloquent\Collection {#1155 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1173 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/42-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1196 …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 {#1182 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1185 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1154 …2} "content" => Illuminate\Database\Eloquent\Collection {#1155 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1173 …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 {#1178 #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" => 1435235 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => 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#hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1166 #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" => 1435236 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/42-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1172 …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 {#1159 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1163 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1165 …2} "content" => Illuminate\Database\Eloquent\Collection {#1164 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1191 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435236 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/42-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1172 …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 {#1159 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection 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#dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№2 (с. 25)
Условие. №2 (с. 25)
скриншот условия
2. Льдина дрейфует относительно берега моря на восток со скоростью, модуль которой равен 3 м/с (рис. 20). С берегом связана система отсчёта $\text{XY}$, ось $\text{X}$ которой направлена на восток, а ось $\text{Y}$ — на север. Система отсчёта $X'Y'$, оси которой параллельны соответствующим осям системы отсчёта $\text{XY}$, связана со льдиной.
Рис. 20
В системе отсчёта $X'Y'$ (относительно льдины) собака перемещается на запад со скоростью, модуль которой равен 1 м/с, человек толкает сани на восток со скоростью, модуль которой равен 2 м/с, а медведь бежит на север со скоростью, модуль которой равен 4 м/с. Заполните таблицу.
Объекты
Величины | Льдина | Сани | Медведь | Собака
Перемещение за 1 с вдоль оси
$X'$ | | | |
$Y'$ | | | |
$\text{X}$ | | | |
$\text{Y}$ | | | |
Проекция скорости
$v_{x'}$ | | | |
$v_{y'}$ | | | |
$v_x$ | | | |
$v_y$ | | | |
Решение. №2 (с. 25)
Дано
Скорость льдины относительно берега (система отсчёта XY), $\vec{V}$: модуль $V = 3$ м/с, направление — на восток.
Скорость собаки относительно льдины (система отсчёта X'Y'), $\vec{v'}_{собака}$: модуль $v'_{собака} = 1$ м/с, направление — на запад.
Скорость саней относительно льдины, $\vec{v'}_{сани}$: модуль $v'_{сани} = 2$ м/с, направление — на восток.
Скорость медведя относительно льдины, $\vec{v'}_{медведь}$: модуль $v'_{медведь} = 4$ м/с, направление — на север.
Промежуток времени, $t = 1$ с.
Ось X и X' направлены на восток (+).
Ось Y и Y' направлены на север (+).
Найти
Для каждого объекта (льдина, сани, медведь, собака) найти:
1. Перемещение за 1 с вдоль осей X', Y', X, Y: $\Delta x'$, $\Delta y'$, $\Delta x$, $\Delta y$.
2. Проекции скорости на оси X', Y', X, Y: $v'_{x}$, $v'_{y}$, $v_{x}$, $v_{y}$.
Решение
В задаче рассматриваются две системы отсчёта:
1. Неподвижная система отсчёта (НСО) $XY$, связанная с берегом.
2. Подвижная система отсчёта (ПСО) $X'Y'$, связанная со льдиной. Эта система движется вместе со льдиной на восток со скоростью $\vec{V}$.
В проекциях на оси скорость ПСО относительно НСО равна: $V_x = 3$ м/с, $V_y = 0$ м/с.
Для нахождения скорости объекта в неподвижной системе отсчёта ($\vec{v}$) используется закон сложения скоростей: $\vec{v} = \vec{v'} + \vec{V}$, где $\vec{v'}$ — скорость объекта в подвижной системе отсчёта. В проекциях на оси это выглядит так:
$v_x = v'_x + V_x$
$v_y = v'_y + V_y$
Перемещение за время $t$ определяется по формуле $\Delta \vec{r} = \vec{v} \cdot t$. Поскольку $t = 1$ с, то проекции перемещения численно равны проекциям скорости: $\Delta x = v_x \cdot 1 = v_x$, $\Delta y = v_y \cdot 1 = v_y$. Аналогично для ПСО: $\Delta x' = v'_x$, $\Delta y' = v'_y$.
Рассчитаем искомые величины для каждого объекта.
Льдина
1. В системе отсчёта X'Y' (относительно самой себя)
Льдина в этой системе неподвижна.
Проекции скорости: $v'_{x, льдина} = 0$ м/с, $v'_{y, льдина} = 0$ м/с.
Перемещение за 1 с: $\Delta x'_{льдина} = 0$ м, $\Delta y'_{льдина} = 0$ м.
2. В системе отсчёта XY (относительно берега)
Льдина движется на восток со скоростью 3 м/с. Это и есть скорость подвижной системы отсчёта.
Проекции скорости: $v_{x, льдина} = V_x = 3$ м/с, $v_{y, льдина} = V_y = 0$ м/с.
Перемещение за 1 с: $\Delta x_{льдина} = 3 \cdot 1 = 3$ м, $\Delta y_{льдина} = 0 \cdot 1 = 0$ м.
Ответ: для льдины: перемещение $\Delta x' = 0$ м, $\Delta y' = 0$ м, $\Delta x = 3$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = 0$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 3$ м/с, $v_{y} = 0$ м/с.
Сани
1. В системе отсчёта X'Y' (относительно льдины)
Сани движутся на восток (положительное направление оси X') со скоростью 2 м/с.
Проекции скорости: $v'_{x, сани} = 2$ м/с, $v'_{y, сани} = 0$ м/с.
Перемещение за 1 с: $\Delta x'_{сани} = 2$ м, $\Delta y'_{сани} = 0$ м.
2. В системе отсчёта XY (относительно берега)
Используем закон сложения скоростей:
Проекции скорости: $v_{x, сани} = v'_{x, сани} + V_x = 2 + 3 = 5$ м/с. $v_{y, сани} = v'_{y, сани} + V_y = 0 + 0 = 0$ м/с.
Перемещение за 1 с: $\Delta x_{сани} = 5 \cdot 1 = 5$ м, $\Delta y_{сани} = 0 \cdot 1 = 0$ м.
Ответ: для саней: перемещение $\Delta x' = 2$ м, $\Delta y' = 0$ м, $\Delta x = 5$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = 2$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 5$ м/с, $v_{y} = 0$ м/с.
Медведь
1. В системе отсчёта X'Y' (относительно льдины)
Медведь бежит на север (положительное направление оси Y') со скоростью 4 м/с.
Проекции скорости: $v'_{x, медведь} = 0$ м/с, $v'_{y, медведь} = 4$ м/с.
Перемещение за 1 с: $\Delta x'_{медведь} = 0$ м, $\Delta y'_{медведь} = 4$ м.
2. В системе отсчёта XY (относительно берега)
Используем закон сложения скоростей:
Проекции скорости: $v_{x, медведь} = v'_{x, медведь} + V_x = 0 + 3 = 3$ м/с. $v_{y, медведь} = v'_{y, медведь} + V_y = 4 + 0 = 4$ м/с.
Перемещение за 1 с: $\Delta x_{медведь} = 3 \cdot 1 = 3$ м, $\Delta y_{медведь} = 4 \cdot 1 = 4$ м.
Ответ: для медведя: перемещение $\Delta x' = 0$ м, $\Delta y' = 4$ м, $\Delta x = 3$ м, $\Delta y = 4$ м; проекции скорости $v'_{x} = 0$ м/с, $v'_{y} = 4$ м/с, $v_{x} = 3$ м/с, $v_{y} = 4$ м/с.
Собака
1. В системе отсчёта X'Y' (относительно льдины)
Собака движется на запад (отрицательное направление оси X') со скоростью 1 м/с.
Проекции скорости: $v'_{x, собака} = -1$ м/с, $v'_{y, собака} = 0$ м/с.
Перемещение за 1 с: $\Delta x'_{собака} = -1$ м, $\Delta y'_{собака} = 0$ м.
2. В системе отсчёта XY (относительно берега)
Используем закон сложения скоростей:
Проекции скорости: $v_{x, собака} = v'_{x, собака} + V_x = -1 + 3 = 2$ м/с. $v_{y, собака} = v'_{y, собака} + V_y = 0 + 0 = 0$ м/с.
Перемещение за 1 с: $\Delta x_{собака} = 2 \cdot 1 = 2$ м, $\Delta y_{собака} = 0 \cdot 1 = 0$ м.
Ответ: для собаки: перемещение $\Delta x' = -1$ м, $\Delta y' = 0$ м, $\Delta x = 2$ м, $\Delta y = 0$ м; проекции скорости $v'_{x} = -1$ м/с, $v'_{y} = 0$ м/с, $v_{x} = 2$ м/с, $v_{y} = 0$ м/с.
Другие задания:
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Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №2 (с. 25), авторов: Грачев (Александр Васильевич), Погожев (Владимир Александрович), Боков (Павел Юрьевич), Вишнякова (Екатерина Анатольевна), 1-й части ФГОС (старый) учебного пособия издательства Просвещение.