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Номер 4, страница 17, 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 3. Прямолинейное равномерное движение по плоскости - номер 4, страница 17.
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" => 1434901 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/03-4" "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 {#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 "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "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" => "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" => 1434811 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное равномерное движение по плоскости" "field_branch_order" => "3" "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" => "14" "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 [ 0 => App\Models\Term {#1129} ] #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 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #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 {#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" => 1434811 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное равномерное движение по плоскости" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "14" "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" => 1698289 "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 [ 0 => App\Models\Term {#1105 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_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" => "1434901" "type" => "task" ] "text" => "<p><strong>4.</strong> На рис. 12 изображена траектория движения по плоскости $\text{XY}$ шайбы, которая через каждые 5 с в результате ударов изменяла направление своего движения.</p><p>Положения шайбы, соответствующие моментам ударов, на рисунке отмечены цифрами 1–5. Часы включили в момент, когда шайба начала движение из точки 1. Определите: а) координаты шайбы в моменты ударов; б) модули перемещений проекций шайбы $\Delta x$, $\Delta y$ от начала движения до соответствующего удара; в) пройденный шайбой путь $\text{s}$ от начала движения до соответствующего удара. Заполните таблицу.</p><p><em>Рис. 12</em></p><p><strong>Моменты ударов</strong> | <strong>$\text{t}$, c</strong> | <strong>$\text{x}$, м</strong> | <strong>$\text{y}$, м</strong> | <strong>$\Delta x$, м</strong> | <strong>$\Delta y$, м</strong> | <strong>$\text{s}$, м</strong></p><p>1 | | | | | |</p><p>2 | | | | | |</p><p>3 | | | | | |</p><p>4 | | | | | |</p><p>5 | | | | | |</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1958" "height" => 1518 "path" => "/media/fizika_09/grachev-rt/0-03/4-1.webp?ts=1759402618" ] ] ] #original: array:7 [ "id" => 1698289 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1434901" "type" => "task" ] "text" => "<p><strong>4.</strong> На рис. 12 изображена траектория движения по плоскости $\text{XY}$ шайбы, которая через каждые 5 с в результате ударов изменяла направление своего движения.</p><p>Положения шайбы, соответствующие моментам ударов, на рисунке отмечены цифрами 1–5. Часы включили в момент, когда шайба начала движение из точки 1. Определите: а) координаты шайбы в моменты ударов; б) модули перемещений проекций шайбы $\Delta x$, $\Delta y$ от начала движения до соответствующего удара; в) пройденный шайбой путь $\text{s}$ от начала движения до соответствующего удара. Заполните таблицу.</p><p><em>Рис. 12</em></p><p><strong>Моменты ударов</strong> | <strong>$\text{t}$, c</strong> | <strong>$\text{x}$, м</strong> | <strong>$\text{y}$, м</strong> | <strong>$\Delta x$, м</strong> | <strong>$\Delta y$, м</strong> | <strong>$\text{s}$, м</strong></p><p>1 | | | | | |</p><p>2 | | | | | |</p><p>3 | | | | | |</p><p>4 | | | | | |</p><p>5 | | | | | |</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1958" "height" => 1518 "path" => "/media/fizika_09/grachev-rt/0-03/4-1.webp?ts=1759402618" ] ] ] #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" => 1734275 "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 [ 0 => App\Models\Term {#1095 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] …6 } ] #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" => "1434901" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Траектория движения шайбы на плоскости XY (рис. 12).<br>Интервал времени между ударами: $Δt = 5 \text{ с}$.<br>Начало отсчета времени ($t=0$) соответствует положению шайбы в точке 1.</p><p>Все данные в условии задачи представлены в системе СИ, перевод не требуется.</p><p><strong>Найти:</strong></p><p>Для каждого момента удара (точки 1, 2, 3, 4, 5) определить:</p><ul> <li>время $t, \text{с}$</li> <li>координаты $x, \text{м}$ и $y, \text{м}$</li> <li>модули проекций перемещения от начала движения $Δx, \text{м}$ и $Δy, \text{м}$</li> <li>пройденный путь от начала движения $s, \text{м}$</li></ul><p><strong>Решение:</strong></p><p>Определим моменты времени для каждого удара, зная, что движение начинается в $t_1=0$ и каждый следующий удар происходит через 5 с.</p><p>$t_1 = 0 \text{ с}$</p><p>$t_2 = t_1 + Δt = 0 + 5 = 5 \text{ с}$</p><p>$t_3 = t_2 + Δt = 5 + 5 = 10 \text{ с}$</p><p>$t_4 = t_3 + Δt = 10 + 5 = 15 \text{ с}$</p><p>$t_5 = t_4 + Δt = 15 + 5 = 20 \text{ с}$</p><p><strong>а) координаты шайбы в моменты ударов</strong></p><p>Координаты ($x, y$) для каждого момента удара определяются по положению соответствующей точки на графике:</p><p>Момент 1: $x_1 = 2 \text{ м}$, $y_1 = 4 \text{ м}$</p><p>Момент 2: $x_2 = 6 \text{ м}$, $y_2 = 1 \text{ м}$</p><p>Момент 3: $x_3 = 2 \text{ м}$, $y_3 = 1 \text{ м}$</p><p>Момент 4: $x_4 = 6 \text{ м}$, $y_4 = 5 \text{ м}$</p><p>Момент 5: $x_5 = 8 \text{ м}$, $y_5 = 3 \text{ м}$</p><p><strong>Ответ:</strong> Координаты ($x, y$) в моменты ударов 1, 2, 3, 4, 5 равны соответственно (2; 4) м, (6; 1) м, (2; 1) м, (6; 5) м, (8; 3) м.</p><p><strong>б) модули перемещений проекций шайбы Δx, Δy от начала движения</strong></p><p>Проекции перемещения $Δx$ и $Δy$ рассчитываются как разность между текущими координатами ($x_k, y_k$) и начальными координатами ($x_1, y_1=2, y_1=4$). Формулы: $Δx_k = x_k - x_1$ и $Δy_k = y_k - y_1$.</p><p>Момент 1 (начало): $Δx_1 = x_1 - x_1 = 2 - 2 = 0 \text{ м}$, $Δy_1 = y_1 - y_1 = 4 - 4 = 0 \text{ м}$</p><p>Момент 2: $Δx_2 = x_2 - x_1 = 6 - 2 = 4 \text{ м}$, $Δy_2 = y_2 - y_1 = 1 - 4 = -3 \text{ м}$</p><p>Момент 3: $Δx_3 = x_3 - x_1 = 2 - 2 = 0 \text{ м}$, $Δy_3 = y_3 - y_1 = 1 - 4 = -3 \text{ м}$</p><p>Момент 4: $Δx_4 = x_4 - x_1 = 6 - 2 = 4 \text{ м}$, $Δy_4 = y_4 - y_1 = 5 - 4 = 1 \text{ м}$</p><p>Момент 5: $Δx_5 = x_5 - x_1 = 8 - 2 = 6 \text{ м}$, $Δy_5 = y_5 - y_1 = 3 - 4 = -1 \text{ м}$</p><p><strong>Ответ:</strong> Проекции перемещений (Δx, Δy) от начала движения в моменты ударов 1, 2, 3, 4, 5 равны соответственно (0; 0) м, (4; -3) м, (0; -3) м, (4; 1) м, (6; -1) м.</p><p><strong>в) пройденный шайбой путь s от начала движения</strong></p><p>Пройденный путь $s$ — это скалярная величина, равная сумме длин всех отрезков траектории от начальной точки. Длина каждого отрезка между точками ($x_a, y_a$) и ($x_b, y_b$) вычисляется по формуле расстояния между двумя точками (основанной на теореме Пифагора): $L = \sqrt{(x_b - x_a)^2 + (y_b - y_a)^2}$.</p><p>Путь до точки 1: $s_1 = 0 \text{ м}$.</p><p>Длина отрезка 1-2: $L_{12} = \sqrt{(6-2)^2 + (1-4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16+9} = \sqrt{25} = 5 \text{ м}$.<br>Путь до точки 2: $s_2 = L_{12} = 5 \text{ м}$.</p><p>Длина отрезка 2-3: $L_{23} = \sqrt{(2-6)^2 + (1-1)^2} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4 \text{ м}$.<br>Путь до точки 3: $s_3 = s_2 + L_{23} = 5 + 4 = 9 \text{ м}$.</p><p>Длина отрезка 3-4: $L_{34} = \sqrt{(6-2)^2 + (5-1)^2} = \sqrt{4^2 + 4^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2} \text{ м}$.<br>Путь до точки 4: $s_4 = s_3 + L_{34} = 9 + 4\sqrt{2} \text{ м}$.</p><p>Длина отрезка 4-5: $L_{45} = \sqrt{(8-6)^2 + (3-5)^2} = \sqrt{2^2 + (-2)^2} = \sqrt{4+4} = \sqrt{8} = 2\sqrt{2} \text{ м}$.<br>Путь до точки 5: $s_5 = s_4 + L_{45} = (9 + 4\sqrt{2}) + 2\sqrt{2} = 9 + 6\sqrt{2} \text{ м}$.</p><p><strong>Ответ:</strong> Пройденный путь $s$ в моменты ударов 1, 2, 3, 4, 5 равен соответственно 0 м, 5 м, 9 м, $9 + 4\sqrt{2}$ м и $9 + 6\sqrt{2}$ м.</p><p>Заполним итоговую таблицу на основе полученных данных.</p><div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"> <thead> <tr> <th style="border: 1px solid rgb(0, 0, 0);">Моменты ударов</th> <th style="border: 1px solid rgb(0, 0, 0);">t, с</th> <th style="border: 1px solid rgb(0, 0, 0);">x, м</th> <th style="border: 1px solid rgb(0, 0, 0);">y, м</th> <th style="border: 1px solid rgb(0, 0, 0);">Δx, м</th> <th style="border: 1px solid rgb(0, 0, 0);">Δy, м</th> <th style="border: 1px solid rgb(0, 0, 0);">s, м</th> </tr> </thead> <tbody> <tr> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> <td style="border: 1px solid rgb(0, 0, 0);">6</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">-3</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">3</td> <td style="border: 1px solid rgb(0, 0, 0);">10</td> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">-3</td> <td style="border: 1px solid rgb(0, 0, 0);">9</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">15</td> <td style="border: 1px solid rgb(0, 0, 0);">6</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">$9 + 4\sqrt{2}$</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">5</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">8</td> <td style="border: 1px solid rgb(0, 0, 0);">3</td> <td style="border: 1px solid rgb(0, 0, 0);">6</td> <td style="border: 1px solid rgb(0, 0, 0);">-1</td> <td style="border: 1px solid rgb(0, 0, 0);">$9 + 6\sqrt{2}$</td> </tr> </tbody></table></div>" ] #original: array:6 [ "id" => 1734275 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1434901" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Траектория движения шайбы на плоскости XY (рис. 12).<br>Интервал времени между ударами: $Δt = 5 \text{ с}$.<br>Начало отсчета времени ($t=0$) соответствует положению шайбы в точке 1.</p><p>Все данные в условии задачи представлены в системе СИ, перевод не требуется.</p><p><strong>Найти:</strong></p><p>Для каждого момента удара (точки 1, 2, 3, 4, 5) определить:</p><ul> <li>время $t, \text{с}$</li> <li>координаты $x, \text{м}$ и $y, \text{м}$</li> <li>модули проекций перемещения от начала движения $Δx, \text{м}$ и $Δy, \text{м}$</li> <li>пройденный путь от начала движения $s, \text{м}$</li></ul><p><strong>Решение:</strong></p><p>Определим моменты времени для каждого удара, зная, что движение начинается в $t_1=0$ и каждый следующий удар происходит через 5 с.</p><p>$t_1 = 0 \text{ с}$</p><p>$t_2 = t_1 + Δt = 0 + 5 = 5 \text{ с}$</p><p>$t_3 = t_2 + Δt = 5 + 5 = 10 \text{ с}$</p><p>$t_4 = t_3 + Δt = 10 + 5 = 15 \text{ с}$</p><p>$t_5 = t_4 + Δt = 15 + 5 = 20 \text{ с}$</p><p><strong>а) координаты шайбы в моменты ударов</strong></p><p>Координаты ($x, y$) для каждого момента удара определяются по положению соответствующей точки на графике:</p><p>Момент 1: $x_1 = 2 \text{ м}$, $y_1 = 4 \text{ м}$</p><p>Момент 2: $x_2 = 6 \text{ м}$, $y_2 = 1 \text{ м}$</p><p>Момент 3: $x_3 = 2 \text{ м}$, $y_3 = 1 \text{ м}$</p><p>Момент 4: $x_4 = 6 \text{ м}$, $y_4 = 5 \text{ м}$</p><p>Момент 5: $x_5 = 8 \text{ м}$, $y_5 = 3 \text{ м}$</p><p><strong>Ответ:</strong> Координаты ($x, y$) в моменты ударов 1, 2, 3, 4, 5 равны соответственно (2; 4) м, (6; 1) м, (2; 1) м, (6; 5) м, (8; 3) м.</p><p><strong>б) модули перемещений проекций шайбы Δx, Δy от начала движения</strong></p><p>Проекции перемещения $Δx$ и $Δy$ рассчитываются как разность между текущими координатами ($x_k, y_k$) и начальными координатами ($x_1, y_1=2, y_1=4$). Формулы: $Δx_k = x_k - x_1$ и $Δy_k = y_k - y_1$.</p><p>Момент 1 (начало): $Δx_1 = x_1 - x_1 = 2 - 2 = 0 \text{ м}$, $Δy_1 = y_1 - y_1 = 4 - 4 = 0 \text{ м}$</p><p>Момент 2: $Δx_2 = x_2 - x_1 = 6 - 2 = 4 \text{ м}$, $Δy_2 = y_2 - y_1 = 1 - 4 = -3 \text{ м}$</p><p>Момент 3: $Δx_3 = x_3 - x_1 = 2 - 2 = 0 \text{ м}$, $Δy_3 = y_3 - y_1 = 1 - 4 = -3 \text{ м}$</p><p>Момент 4: $Δx_4 = x_4 - x_1 = 6 - 2 = 4 \text{ м}$, $Δy_4 = y_4 - y_1 = 5 - 4 = 1 \text{ м}$</p><p>Момент 5: $Δx_5 = x_5 - x_1 = 8 - 2 = 6 \text{ м}$, $Δy_5 = y_5 - y_1 = 3 - 4 = -1 \text{ м}$</p><p><strong>Ответ:</strong> Проекции перемещений (Δx, Δy) от начала движения в моменты ударов 1, 2, 3, 4, 5 равны соответственно (0; 0) м, (4; -3) м, (0; -3) м, (4; 1) м, (6; -1) м.</p><p><strong>в) пройденный шайбой путь s от начала движения</strong></p><p>Пройденный путь $s$ — это скалярная величина, равная сумме длин всех отрезков траектории от начальной точки. Длина каждого отрезка между точками ($x_a, y_a$) и ($x_b, y_b$) вычисляется по формуле расстояния между двумя точками (основанной на теореме Пифагора): $L = \sqrt{(x_b - x_a)^2 + (y_b - y_a)^2}$.</p><p>Путь до точки 1: $s_1 = 0 \text{ м}$.</p><p>Длина отрезка 1-2: $L_{12} = \sqrt{(6-2)^2 + (1-4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16+9} = \sqrt{25} = 5 \text{ м}$.<br>Путь до точки 2: $s_2 = L_{12} = 5 \text{ м}$.</p><p>Длина отрезка 2-3: $L_{23} = \sqrt{(2-6)^2 + (1-1)^2} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4 \text{ м}$.<br>Путь до точки 3: $s_3 = s_2 + L_{23} = 5 + 4 = 9 \text{ м}$.</p><p>Длина отрезка 3-4: $L_{34} = \sqrt{(6-2)^2 + (5-1)^2} = \sqrt{4^2 + 4^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2} \text{ м}$.<br>Путь до точки 4: $s_4 = s_3 + L_{34} = 9 + 4\sqrt{2} \text{ м}$.</p><p>Длина отрезка 4-5: $L_{45} = \sqrt{(8-6)^2 + (3-5)^2} = \sqrt{2^2 + (-2)^2} = \sqrt{4+4} = \sqrt{8} = 2\sqrt{2} \text{ м}$.<br>Путь до точки 5: $s_5 = s_4 + L_{45} = (9 + 4\sqrt{2}) + 2\sqrt{2} = 9 + 6\sqrt{2} \text{ м}$.</p><p><strong>Ответ:</strong> Пройденный путь $s$ в моменты ударов 1, 2, 3, 4, 5 равен соответственно 0 м, 5 м, 9 м, $9 + 4\sqrt{2}$ м и $9 + 6\sqrt{2}$ м.</p><p>Заполним итоговую таблицу на основе полученных данных.</p><div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"> <thead> <tr> <th style="border: 1px solid rgb(0, 0, 0);">Моменты ударов</th> <th style="border: 1px solid rgb(0, 0, 0);">t, с</th> <th style="border: 1px solid rgb(0, 0, 0);">x, м</th> <th style="border: 1px solid rgb(0, 0, 0);">y, м</th> <th style="border: 1px solid rgb(0, 0, 0);">Δx, м</th> <th style="border: 1px solid rgb(0, 0, 0);">Δy, м</th> <th style="border: 1px solid rgb(0, 0, 0);">s, м</th> </tr> </thead> <tbody> <tr> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> <td style="border: 1px solid rgb(0, 0, 0);">6</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">-3</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">3</td> <td style="border: 1px solid rgb(0, 0, 0);">10</td> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">-3</td> <td style="border: 1px solid rgb(0, 0, 0);">9</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">15</td> <td style="border: 1px solid rgb(0, 0, 0);">6</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">$9 + 4\sqrt{2}$</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">5</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">8</td> <td style="border: 1px solid rgb(0, 0, 0);">3</td> <td style="border: 1px solid rgb(0, 0, 0);">6</td> <td style="border: 1px solid rgb(0, 0, 0);">-1</td> <td style="border: 1px solid rgb(0, 0, 0);">$9 + 6\sqrt{2}$</td> </tr> </tbody></table></div>" ] #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" 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№4 (с. 17)
Условие. №4 (с. 17)
скриншот условия
4. На рис. 12 изображена траектория движения по плоскости $\text{XY}$ шайбы, которая через каждые 5 с в результате ударов изменяла направление своего движения.
Положения шайбы, соответствующие моментам ударов, на рисунке отмечены цифрами 1–5. Часы включили в момент, когда шайба начала движение из точки 1. Определите: а) координаты шайбы в моменты ударов; б) модули перемещений проекций шайбы $\Delta x$, $\Delta y$ от начала движения до соответствующего удара; в) пройденный шайбой путь $\text{s}$ от начала движения до соответствующего удара. Заполните таблицу.
Рис. 12
Моменты ударов | $\text{t}$, c | $\text{x}$, м | $\text{y}$, м | $\Delta x$, м | $\Delta y$, м | $\text{s}$, м
1 | | | | | |
2 | | | | | |
3 | | | | | |
4 | | | | | |
5 | | | | | |
Решение. №4 (с. 17)
Дано:
Траектория движения шайбы на плоскости XY (рис. 12).
Интервал времени между ударами: $Δt = 5 \text{ с}$.
Начало отсчета времени ($t=0$) соответствует положению шайбы в точке 1.
Все данные в условии задачи представлены в системе СИ, перевод не требуется.
Найти:
Для каждого момента удара (точки 1, 2, 3, 4, 5) определить:
- время $t, \text{с}$
- координаты $x, \text{м}$ и $y, \text{м}$
- модули проекций перемещения от начала движения $Δx, \text{м}$ и $Δy, \text{м}$
- пройденный путь от начала движения $s, \text{м}$
Решение:
Определим моменты времени для каждого удара, зная, что движение начинается в $t_1=0$ и каждый следующий удар происходит через 5 с.
$t_1 = 0 \text{ с}$
$t_2 = t_1 + Δt = 0 + 5 = 5 \text{ с}$
$t_3 = t_2 + Δt = 5 + 5 = 10 \text{ с}$
$t_4 = t_3 + Δt = 10 + 5 = 15 \text{ с}$
$t_5 = t_4 + Δt = 15 + 5 = 20 \text{ с}$
а) координаты шайбы в моменты ударов
Координаты ($x, y$) для каждого момента удара определяются по положению соответствующей точки на графике:
Момент 1: $x_1 = 2 \text{ м}$, $y_1 = 4 \text{ м}$
Момент 2: $x_2 = 6 \text{ м}$, $y_2 = 1 \text{ м}$
Момент 3: $x_3 = 2 \text{ м}$, $y_3 = 1 \text{ м}$
Момент 4: $x_4 = 6 \text{ м}$, $y_4 = 5 \text{ м}$
Момент 5: $x_5 = 8 \text{ м}$, $y_5 = 3 \text{ м}$
Ответ: Координаты ($x, y$) в моменты ударов 1, 2, 3, 4, 5 равны соответственно (2; 4) м, (6; 1) м, (2; 1) м, (6; 5) м, (8; 3) м.
б) модули перемещений проекций шайбы Δx, Δy от начала движения
Проекции перемещения $Δx$ и $Δy$ рассчитываются как разность между текущими координатами ($x_k, y_k$) и начальными координатами ($x_1, y_1=2, y_1=4$). Формулы: $Δx_k = x_k - x_1$ и $Δy_k = y_k - y_1$.
Момент 1 (начало): $Δx_1 = x_1 - x_1 = 2 - 2 = 0 \text{ м}$, $Δy_1 = y_1 - y_1 = 4 - 4 = 0 \text{ м}$
Момент 2: $Δx_2 = x_2 - x_1 = 6 - 2 = 4 \text{ м}$, $Δy_2 = y_2 - y_1 = 1 - 4 = -3 \text{ м}$
Момент 3: $Δx_3 = x_3 - x_1 = 2 - 2 = 0 \text{ м}$, $Δy_3 = y_3 - y_1 = 1 - 4 = -3 \text{ м}$
Момент 4: $Δx_4 = x_4 - x_1 = 6 - 2 = 4 \text{ м}$, $Δy_4 = y_4 - y_1 = 5 - 4 = 1 \text{ м}$
Момент 5: $Δx_5 = x_5 - x_1 = 8 - 2 = 6 \text{ м}$, $Δy_5 = y_5 - y_1 = 3 - 4 = -1 \text{ м}$
Ответ: Проекции перемещений (Δx, Δy) от начала движения в моменты ударов 1, 2, 3, 4, 5 равны соответственно (0; 0) м, (4; -3) м, (0; -3) м, (4; 1) м, (6; -1) м.
в) пройденный шайбой путь s от начала движения
Пройденный путь $s$ — это скалярная величина, равная сумме длин всех отрезков траектории от начальной точки. Длина каждого отрезка между точками ($x_a, y_a$) и ($x_b, y_b$) вычисляется по формуле расстояния между двумя точками (основанной на теореме Пифагора): $L = \sqrt{(x_b - x_a)^2 + (y_b - y_a)^2}$.
Путь до точки 1: $s_1 = 0 \text{ м}$.
Длина отрезка 1-2: $L_{12} = \sqrt{(6-2)^2 + (1-4)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16+9} = \sqrt{25} = 5 \text{ м}$.
Путь до точки 2: $s_2 = L_{12} = 5 \text{ м}$.
Длина отрезка 2-3: $L_{23} = \sqrt{(2-6)^2 + (1-1)^2} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4 \text{ м}$.
Путь до точки 3: $s_3 = s_2 + L_{23} = 5 + 4 = 9 \text{ м}$.
Длина отрезка 3-4: $L_{34} = \sqrt{(6-2)^2 + (5-1)^2} = \sqrt{4^2 + 4^2} = \sqrt{16+16} = \sqrt{32} = 4\sqrt{2} \text{ м}$.
Путь до точки 4: $s_4 = s_3 + L_{34} = 9 + 4\sqrt{2} \text{ м}$.
Длина отрезка 4-5: $L_{45} = \sqrt{(8-6)^2 + (3-5)^2} = \sqrt{2^2 + (-2)^2} = \sqrt{4+4} = \sqrt{8} = 2\sqrt{2} \text{ м}$.
Путь до точки 5: $s_5 = s_4 + L_{45} = (9 + 4\sqrt{2}) + 2\sqrt{2} = 9 + 6\sqrt{2} \text{ м}$.
Ответ: Пройденный путь $s$ в моменты ударов 1, 2, 3, 4, 5 равен соответственно 0 м, 5 м, 9 м, $9 + 4\sqrt{2}$ м и $9 + 6\sqrt{2}$ м.
Заполним итоговую таблицу на основе полученных данных.
| Моменты ударов | t, с | x, м | y, м | Δx, м | Δy, м | s, м |
|---|---|---|---|---|---|---|
| 1 | 0 | 2 | 4 | 0 | 0 | 0 |
| 2 | 5 | 6 | 1 | 4 | -3 | 5 |
| 3 | 10 | 2 | 1 | 0 | -3 | 9 |
| 4 | 15 | 6 | 5 | 4 | 1 | $9 + 4\sqrt{2}$ |
| 5 | 20 | 8 | 3 | 6 | -1 | $9 + 6\sqrt{2}$ |
Другие задания:
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