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Номер 4, страница 39, 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 9. Движение тела, брошенного под углом к горизонту - номер 4, страница 39.
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" => 1434936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/09-4" "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 [ …6] "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 [ …6] "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 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "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 [ …6] "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 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "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 [ …6] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 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 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "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" => 1434817 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Движение тела, брошенного под углом к горизонту" "field_branch_order" => "9" "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 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "37" "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 …2} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1147 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 …2} ] #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 …2} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1147 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434817 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Движение тела, брошенного под углом к горизонту" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "37" "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" => 1698324 "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 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 …2} "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 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1434936" "type" => "task" ] "text" => "<p><strong>4.</strong> Тело, брошенное из начала координат под углом к горизонтальной оси $\text{X}$, совершает свободное падение.</p><p>Ось $\text{Y}$ направлена вертикально вверх. Начальная скорость $\vec{v}$ тела такова, что её проекция на ось $\text{X}$ равна $\text{20}$ м/с, а на ось $\text{Y}$ равна $\text{30}$ м/с.</p><p>Заполните таблицу, определив требуемые величины в заданные моменты времени, а затем изобразите на плоскости $\text{XY}$ (рис. 31) траекторию этого тела и векторы скорости тела в соответствующие моменты времени.</p><p>Рис. 31</p><p><strong>Момент времени $\text{t}$, с</strong>: 0, 1, 2, 3, 4, 5</p><p><strong>Проекция скорости тела на ось $\text{X}$, м/с</strong>: , , , , ,</p><p><strong>Проекция скорости тела на ось $\text{Y}$, м/с</strong>: , , , , ,</p><p><strong>Координата тела $\text{x}$, м</strong>: , , , , ,</p><p><strong>Координата тела $\text{y}$, м</strong>: , , , , ,</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1949" "height" => 1464 "path" => "/media/fizika_09/grachev-rt/0-09/4-1.webp?ts=1759402648" ] ] ] #original: array:7 [ "id" => 1698324 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1434936" "type" => "task" ] "text" => "<p><strong>4.</strong> Тело, брошенное из начала координат под углом к горизонтальной оси $\text{X}$, совершает свободное падение.</p><p>Ось $\text{Y}$ направлена вертикально вверх. Начальная скорость $\vec{v}$ тела такова, что её проекция на ось $\text{X}$ равна $\text{20}$ м/с, а на ось $\text{Y}$ равна $\text{30}$ м/с.</p><p>Заполните таблицу, определив требуемые величины в заданные моменты времени, а затем изобразите на плоскости $\text{XY}$ (рис. 31) траекторию этого тела и векторы скорости тела в соответствующие моменты времени.</p><p>Рис. 31</p><p><strong>Момент времени $\text{t}$, с</strong>: 0, 1, 2, 3, 4, 5</p><p><strong>Проекция скорости тела на ось $\text{X}$, м/с</strong>: , , , , ,</p><p><strong>Проекция скорости тела на ось $\text{Y}$, м/с</strong>: , , , , ,</p><p><strong>Координата тела $\text{x}$, м</strong>: , , , , ,</p><p><strong>Координата тела $\text{y}$, м</strong>: , , , , ,</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1949" "height" => 1464 "path" => "/media/fizika_09/grachev-rt/0-09/4-1.webp?ts=1759402648" ] ] ] #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" => 1734310 "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 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "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 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1434936" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Движение тела в поле тяжести Земли (свободное падение).</p> <p>Начальные координаты: $x_0 = 0$ м, $y_0 = 0$ м.</p> <p>Проекции начальной скорости: $v_{0x} = 20$ м/с, $v_{0y} = 30$ м/с.</p> <p>Ось X направлена горизонтально, ось Y — вертикально вверх.</p> <p>Ускорение свободного падения принимаем равным $g \approx 10$ м/с².</p> <p>Все данные уже представлены в системе СИ.</p> <p><strong>Найти:</strong></p> <p>1. Значения проекций скорости ($v_x, v_y$) и координат ($x, y$) тела в моменты времени $t$ от 0 до 5 с.</p> <p>2. Построить траекторию движения тела и изобразить векторы скорости в указанные моменты времени на плоскости XY.</p> <p><strong>Решение:</strong></p> <p>Движение тела, брошенного под углом к горизонту, можно разложить на два независимых движения: равномерное движение вдоль горизонтальной оси X и равноускоренное движение вдоль вертикальной оси Y с ускорением $a_y = -g$.</p> <p>Уравнения движения:</p> <ul> <li> <p>Для оси X (равномерное движение):</p> <p>Проекция скорости: $v_x(t) = v_{0x}$</p> <p>Координата: $x(t) = x_0 + v_{0x}t$</p> </li> <li> <p>Для оси Y (равноускоренное движение):</p> <p>Проекция скорости: $v_y(t) = v_{0y} - gt$</p> <p>Координата: $y(t) = y_0 + v_{0y}t - \frac{gt^2}{2}$</p> </li> </ul> <p>Подставим известные значения ($x_0=0, y_0=0, v_{0x}=20, v_{0y}=30, g=10$):</p> <ul> <li>$v_x(t) = 20$ (м/с)</li> <li>$x(t) = 20t$ (м)</li> <li>$v_y(t) = 30 - 10t$ (м/с)</li> <li>$y(t) = 30t - 5t^2$ (м)</li> </ul> <p><strong>1. Заполнение таблицы</strong></p> <p>Вычислим требуемые величины для каждого момента времени от $t=0$ до $t=5$ с.</p> <ul> <li> <p>При $t=0$ с:</p> <p>$v_x(0) = 20$ м/с</p> <p>$v_y(0) = 30 - 10 \cdot 0 = 30$ м/с</p> <p>$x(0) = 20 \cdot 0 = 0$ м</p> <p>$y(0) = 30 \cdot 0 - 5 \cdot 0^2 = 0$ м</p> </li> <li> <p>При $t=1$ с:</p> <p>$v_x(1) = 20$ м/с</p> <p>$v_y(1) = 30 - 10 \cdot 1 = 20$ м/с</p> <p>$x(1) = 20 \cdot 1 = 20$ м</p> <p>$y(1) = 30 \cdot 1 - 5 \cdot 1^2 = 30 - 5 = 25$ м</p> </li> <li> <p>При $t=2$ с:</p> <p>$v_x(2) = 20$ м/с</p> <p>$v_y(2) = 30 - 10 \cdot 2 = 10$ м/с</p> <p>$x(2) = 20 \cdot 2 = 40$ м</p> <p>$y(2) = 30 \cdot 2 - 5 \cdot 2^2 = 60 - 20 = 40$ м</p> </li> <li> <p>При $t=3$ с:</p> <p>$v_x(3) = 20$ м/с</p> <p>$v_y(3) = 30 - 10 \cdot 3 = 0$ м/с</p> <p>$x(3) = 20 \cdot 3 = 60$ м</p> <p>$y(3) = 30 \cdot 3 - 5 \cdot 3^2 = 90 - 45 = 45$ м (высшая точка траектории)</p> </li> <li> <p>При $t=4$ с:</p> <p>$v_x(4) = 20$ м/с</p> <p>$v_y(4) = 30 - 10 \cdot 4 = -10$ м/с</p> <p>$x(4) = 20 \cdot 4 = 80$ м</p> <p>$y(4) = 30 \cdot 4 - 5 \cdot 4^2 = 120 - 80 = 40$ м</p> </li> <li> <p>При $t=5$ с:</p> <p>$v_x(5) = 20$ м/с</p> <p>$v_y(5) = 30 - 10 \cdot 5 = -20$ м/с</p> <p>$x(5) = 20 \cdot 5 = 100$ м</p> <p>$y(5) = 30 \cdot 5 - 5 \cdot 5^2 = 150 - 125 = 25$ м</p> </li> </ul> <p>Сведем результаты в таблицу:</p> <div class="table-wrap"><table border="1" cellpadding="5" cellspacing="0" style="border: 1px solid rgb(0, 0, 0);"> <tbody> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Момент времени t, с</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">3</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Проекция скорости тела на ось X, м/с</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Проекция скорости тела на ось Y, м/с</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">30</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">10</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">-10</td> <td style="border: 1px solid rgb(0, 0, 0);">-20</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Координата тела x, м</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">40</td> <td style="border: 1px solid rgb(0, 0, 0);">60</td> <td style="border: 1px solid rgb(0, 0, 0);">80</td> <td style="border: 1px solid rgb(0, 0, 0);">100</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Координата тела y, м</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">25</td> <td style="border: 1px solid rgb(0, 0, 0);">40</td> <td style="border: 1px solid rgb(0, 0, 0);">45</td> <td style="border: 1px solid rgb(0, 0, 0);">40</td> <td style="border: 1px solid rgb(0, 0, 0);">25</td> </tr> </tbody> </table></div> <p><strong>Ответ:</strong> Заполненная таблица представлена выше.</p> <p><strong>2. Построение графика траектории и векторов скорости</strong></p> <p>Используя вычисленные координаты ($x, y$), строим траекторию движения тела. В каждой точке, соответствующей моментам времени $t=0, 1, 2, 3, 4, 5$ с, строим вектор скорости $\vec{v}$, компонентами которого являются вычисленные значения $v_x$ и $v_y$. Вектор скорости всегда направлен по касательной к траектории.</p> <svg width="600" height="300" viewBox="-10 -10 130 60" xmlns="http://www.w3.org/2000/svg" style="background-color: #fdfdfd;"> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="black"></polygon> </marker> <marker id="arrowhead_v" markerWidth="5" markerHeight="3.5" refX="5" refY="1.75" orient="auto"> <polygon points="0 0, 5 1.75, 0 3.5" fill="red"></polygon> </marker> </defs> <!-- Grid --> <g stroke="#cccccc" stroke-width="0.5" stroke-dasharray="2,2"> <path d="M 20 0 v 50 M 40 0 v 50 M 60 0 v 50 M 80 0 v 50 M 100 0 v 50 M 120 0 v 50"></path> <path d="M 0 5 h 125 M 0 10 h 125 M 0 15 h 125 M 0 20 h 125 M 0 25 h 125 M 0 30 h 125 M 0 35 h 125 M 0 40 h 125 M 0 45 h 125"></path> </g> <!-- Axes --> <g stroke="black" stroke-width="1"> <line x1="0" y1="0" x2="125" y2="0" marker-end="url(#arrowhead)"></line> <line x1="0" y1="0" x2="0" y2="50" marker-end="url(#arrowhead)"></line> </g> <!-- Axis Labels and Ticks --> <g font-family="sans-serif" font-size="5"> <text x="126" y="2" fill="black">X, м</text> <text x="2" y="52" fill="black">Y, м</text> <g text-anchor="middle" dominant-baseline="hanging"> <text x="20" y="-4">20</text> <text x="40" y="-4">40</text> <text x="60" y="-4">60</text> <text x="80" y="-4">80</text> <text x="100" y="-4">100</text> <text x="120" y="-4">120</text> </g> <g text-anchor="end" dominant-baseline="middle"> <text x="-1" y="5">5</text> <text x="-1" y="10">10</text> <text x="-1" y="15">15</text> <text x="-1" y="20">20</text> <text x="-1" y="25">25</text> <text x="-1" y="30">30</text> <text x="-1" y="35">35</text> <text x="-1" y="40">40</text> <text x="-1" y="45">45</text> </g> <text x="0" y="-4" text-anchor="middle" dominant-baseline="hanging">0</text> </g> <!-- Trajectory --> <path d="M 0,0 C 10,15 30,40 60,45 C 90,50 90,25 100,25" stroke="blue" stroke-width="1.5" fill="none"></path> <!-- Points --> <g fill="blue"> <circle cx="0" cy="0" r="1"></circle> <circle cx="20" cy="25" r="1"></circle> <circle cx="40" cy="40" r="1"></circle> <circle cx="60" cy="45" r="1"></circle> <circle cx="80" cy="40" r="1"></circle> <circle cx="100" cy="25" r="1"></circle> </g> <!-- Velocity Vectors (scaled by 0.7 for visibility) --> <g stroke="red" stroke-width="1" marker-end="url(#arrowhead_v)"> <line x1="0" y1="0" x2="14" y2="21"></line> <line x1="20" y1="25" x2="34" y2="39"></line> <line x1="40" y1="40" x2="54" y2="47"></line> <line x1="60" y1="45" x2="74" y2="45"></line> <line x1="80" y1="40" x2="94" y2="33"></line> <line x1="100" y1="25" x2="114" y2="11"></line> </g> <g fill="red" font-size="4px" font-family="sans-serif"> <text x="15" y="21">v₀</text> <text x="35" y="39">v₁</text> <text x="55" y="49">v₂</text> <text x="75" y="45">v₃</text> <text x="95" y="33">v₄</text> <text x="115" y="11">v₅</text> </g> </svg> <p><strong>Ответ:</strong> График траектории (синяя кривая) и векторов скорости (красные стрелки) в моменты времени $t = 0, 1, 2, 3, 4, 5$ с показан на рисунке выше.</p>" ] #original: array:6 [ "id" => 1734310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1434936" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Движение тела в поле тяжести Земли (свободное падение).</p> <p>Начальные координаты: $x_0 = 0$ м, $y_0 = 0$ м.</p> <p>Проекции начальной скорости: $v_{0x} = 20$ м/с, $v_{0y} = 30$ м/с.</p> <p>Ось X направлена горизонтально, ось Y — вертикально вверх.</p> <p>Ускорение свободного падения принимаем равным $g \approx 10$ м/с².</p> <p>Все данные уже представлены в системе СИ.</p> <p><strong>Найти:</strong></p> <p>1. Значения проекций скорости ($v_x, v_y$) и координат ($x, y$) тела в моменты времени $t$ от 0 до 5 с.</p> <p>2. Построить траекторию движения тела и изобразить векторы скорости в указанные моменты времени на плоскости XY.</p> <p><strong>Решение:</strong></p> <p>Движение тела, брошенного под углом к горизонту, можно разложить на два независимых движения: равномерное движение вдоль горизонтальной оси X и равноускоренное движение вдоль вертикальной оси Y с ускорением $a_y = -g$.</p> <p>Уравнения движения:</p> <ul> <li> <p>Для оси X (равномерное движение):</p> <p>Проекция скорости: $v_x(t) = v_{0x}$</p> <p>Координата: $x(t) = x_0 + v_{0x}t$</p> </li> <li> <p>Для оси Y (равноускоренное движение):</p> <p>Проекция скорости: $v_y(t) = v_{0y} - gt$</p> <p>Координата: $y(t) = y_0 + v_{0y}t - \frac{gt^2}{2}$</p> </li> </ul> <p>Подставим известные значения ($x_0=0, y_0=0, v_{0x}=20, v_{0y}=30, g=10$):</p> <ul> <li>$v_x(t) = 20$ (м/с)</li> <li>$x(t) = 20t$ (м)</li> <li>$v_y(t) = 30 - 10t$ (м/с)</li> <li>$y(t) = 30t - 5t^2$ (м)</li> </ul> <p><strong>1. Заполнение таблицы</strong></p> <p>Вычислим требуемые величины для каждого момента времени от $t=0$ до $t=5$ с.</p> <ul> <li> <p>При $t=0$ с:</p> <p>$v_x(0) = 20$ м/с</p> <p>$v_y(0) = 30 - 10 \cdot 0 = 30$ м/с</p> <p>$x(0) = 20 \cdot 0 = 0$ м</p> <p>$y(0) = 30 \cdot 0 - 5 \cdot 0^2 = 0$ м</p> </li> <li> <p>При $t=1$ с:</p> <p>$v_x(1) = 20$ м/с</p> <p>$v_y(1) = 30 - 10 \cdot 1 = 20$ м/с</p> <p>$x(1) = 20 \cdot 1 = 20$ м</p> <p>$y(1) = 30 \cdot 1 - 5 \cdot 1^2 = 30 - 5 = 25$ м</p> </li> <li> <p>При $t=2$ с:</p> <p>$v_x(2) = 20$ м/с</p> <p>$v_y(2) = 30 - 10 \cdot 2 = 10$ м/с</p> <p>$x(2) = 20 \cdot 2 = 40$ м</p> <p>$y(2) = 30 \cdot 2 - 5 \cdot 2^2 = 60 - 20 = 40$ м</p> </li> <li> <p>При $t=3$ с:</p> <p>$v_x(3) = 20$ м/с</p> <p>$v_y(3) = 30 - 10 \cdot 3 = 0$ м/с</p> <p>$x(3) = 20 \cdot 3 = 60$ м</p> <p>$y(3) = 30 \cdot 3 - 5 \cdot 3^2 = 90 - 45 = 45$ м (высшая точка траектории)</p> </li> <li> <p>При $t=4$ с:</p> <p>$v_x(4) = 20$ м/с</p> <p>$v_y(4) = 30 - 10 \cdot 4 = -10$ м/с</p> <p>$x(4) = 20 \cdot 4 = 80$ м</p> <p>$y(4) = 30 \cdot 4 - 5 \cdot 4^2 = 120 - 80 = 40$ м</p> </li> <li> <p>При $t=5$ с:</p> <p>$v_x(5) = 20$ м/с</p> <p>$v_y(5) = 30 - 10 \cdot 5 = -20$ м/с</p> <p>$x(5) = 20 \cdot 5 = 100$ м</p> <p>$y(5) = 30 \cdot 5 - 5 \cdot 5^2 = 150 - 125 = 25$ м</p> </li> </ul> <p>Сведем результаты в таблицу:</p> <div class="table-wrap"><table border="1" cellpadding="5" cellspacing="0" style="border: 1px solid rgb(0, 0, 0);"> <tbody> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Момент времени t, с</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">1</td> <td style="border: 1px solid rgb(0, 0, 0);">2</td> <td style="border: 1px solid rgb(0, 0, 0);">3</td> <td style="border: 1px solid rgb(0, 0, 0);">4</td> <td style="border: 1px solid rgb(0, 0, 0);">5</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Проекция скорости тела на ось X, м/с</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Проекция скорости тела на ось Y, м/с</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">30</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">10</td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">-10</td> <td style="border: 1px solid rgb(0, 0, 0);">-20</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Координата тела x, м</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">20</td> <td style="border: 1px solid rgb(0, 0, 0);">40</td> <td style="border: 1px solid rgb(0, 0, 0);">60</td> <td style="border: 1px solid rgb(0, 0, 0);">80</td> <td style="border: 1px solid rgb(0, 0, 0);">100</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);"><strong>Координата тела y, м</strong></td> <td style="border: 1px solid rgb(0, 0, 0);">0</td> <td style="border: 1px solid rgb(0, 0, 0);">25</td> <td style="border: 1px solid rgb(0, 0, 0);">40</td> <td style="border: 1px solid rgb(0, 0, 0);">45</td> <td style="border: 1px solid rgb(0, 0, 0);">40</td> <td style="border: 1px solid rgb(0, 0, 0);">25</td> </tr> </tbody> </table></div> <p><strong>Ответ:</strong> Заполненная таблица представлена выше.</p> <p><strong>2. Построение графика траектории и векторов скорости</strong></p> <p>Используя вычисленные координаты ($x, y$), строим траекторию движения тела. В каждой точке, соответствующей моментам времени $t=0, 1, 2, 3, 4, 5$ с, строим вектор скорости $\vec{v}$, компонентами которого являются вычисленные значения $v_x$ и $v_y$. Вектор скорости всегда направлен по касательной к траектории.</p> <svg width="600" height="300" viewBox="-10 -10 130 60" xmlns="http://www.w3.org/2000/svg" style="background-color: #fdfdfd;"> <defs> <marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"> <polygon points="0 0, 10 3.5, 0 7" fill="black"></polygon> </marker> <marker id="arrowhead_v" markerWidth="5" markerHeight="3.5" refX="5" refY="1.75" orient="auto"> <polygon points="0 0, 5 1.75, 0 3.5" fill="red"></polygon> </marker> </defs> <!-- Grid --> <g stroke="#cccccc" stroke-width="0.5" stroke-dasharray="2,2"> <path d="M 20 0 v 50 M 40 0 v 50 M 60 0 v 50 M 80 0 v 50 M 100 0 v 50 M 120 0 v 50"></path> <path d="M 0 5 h 125 M 0 10 h 125 M 0 15 h 125 M 0 20 h 125 M 0 25 h 125 M 0 30 h 125 M 0 35 h 125 M 0 40 h 125 M 0 45 h 125"></path> </g> <!-- Axes --> <g stroke="black" stroke-width="1"> <line x1="0" y1="0" x2="125" y2="0" marker-end="url(#arrowhead)"></line> <line x1="0" y1="0" x2="0" y2="50" 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fill="blue"> <circle cx="0" cy="0" r="1"></circle> <circle cx="20" cy="25" r="1"></circle> <circle cx="40" cy="40" r="1"></circle> <circle cx="60" cy="45" r="1"></circle> <circle cx="80" cy="40" r="1"></circle> <circle cx="100" cy="25" r="1"></circle> </g> <!-- Velocity Vectors (scaled by 0.7 for visibility) --> <g stroke="red" stroke-width="1" marker-end="url(#arrowhead_v)"> <line x1="0" y1="0" x2="14" y2="21"></line> <line x1="20" y1="25" x2="34" y2="39"></line> <line x1="40" y1="40" x2="54" y2="47"></line> <line x1="60" y1="45" x2="74" y2="45"></line> <line x1="80" y1="40" x2="94" y2="33"></line> <line x1="100" y1="25" x2="114" y2="11"></line> </g> <g fill="red" font-size="4px" font-family="sans-serif"> <text x="15" y="21">v₀</text> <text x="35" y="39">v₁</text> <text x="55" y="49">v₂</text> <text x="75" y="45">v₃</text> <text x="95" y="33">v₄</text> <text x="115" y="11">v₅</text> </g> </svg> <p><strong>Ответ:</strong> График траектории (синяя кривая) и векторов скорости (красные 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"field_task_type" => Illuminate\Database\Eloquent\Collection {#1182 …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 {#1183 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1184 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265 …2} "content" => Illuminate\Database\Eloquent\Collection {#1222 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1256 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1258 #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" => 1435280 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1272 …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 {#1255 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1262 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259 …2} "content" => Illuminate\Database\Eloquent\Collection {#1263 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1245 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435280 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1272 …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 {#1255 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1262 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259 …2} "content" => Illuminate\Database\Eloquent\Collection {#1263 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1245 …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 {#1251 #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" => 1435281 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226 …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 {#1244 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1247 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1234 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435281 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226 …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 {#1244 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1247 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1234 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1238 #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" => 1435282 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1232 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1236 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1233 …2} "content" => Illuminate\Database\Eloquent\Collection {#1237 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435282 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1232 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1236 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1233 …2} "content" => Illuminate\Database\Eloquent\Collection {#1237 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1260 #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" => 1435283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1235 …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 {#1188 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1223 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1225 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1211 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1235 …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 {#1188 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1223 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1225 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1211 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1217 #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" => 1435284 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1224 …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 {#1210 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1213 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1216 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1196 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435284 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/46-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1224 …2} …15 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1435674 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-39" "field_display_title" => "39" "field_folder" => "3" "field_image_name" => "39" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1162} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1160} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1161} "content" => Illuminate\Database\Eloquent\Collection {#1172} "next" => array:2 [ "refs" => "1435675" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435673" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1165} ] #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" => 1434936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "39" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/09-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1114} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1434937" "type" => "task" ] "previous" => array:2 [ "refs" => "1434935" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109} "page" => array:2 [ "refs" => "1435674" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№4 (с. 39)
Условие. №4 (с. 39)
скриншот условия
4. Тело, брошенное из начала координат под углом к горизонтальной оси $\text{X}$, совершает свободное падение.
Ось $\text{Y}$ направлена вертикально вверх. Начальная скорость $\vec{v}$ тела такова, что её проекция на ось $\text{X}$ равна $\text{20}$ м/с, а на ось $\text{Y}$ равна $\text{30}$ м/с.
Заполните таблицу, определив требуемые величины в заданные моменты времени, а затем изобразите на плоскости $\text{XY}$ (рис. 31) траекторию этого тела и векторы скорости тела в соответствующие моменты времени.
Рис. 31
Момент времени $\text{t}$, с: 0, 1, 2, 3, 4, 5
Проекция скорости тела на ось $\text{X}$, м/с: , , , , ,
Проекция скорости тела на ось $\text{Y}$, м/с: , , , , ,
Координата тела $\text{x}$, м: , , , , ,
Координата тела $\text{y}$, м: , , , , ,
Решение. №4 (с. 39)
Дано:
Движение тела в поле тяжести Земли (свободное падение).
Начальные координаты: $x_0 = 0$ м, $y_0 = 0$ м.
Проекции начальной скорости: $v_{0x} = 20$ м/с, $v_{0y} = 30$ м/с.
Ось X направлена горизонтально, ось Y — вертикально вверх.
Ускорение свободного падения принимаем равным $g \approx 10$ м/с².
Все данные уже представлены в системе СИ.
Найти:
1. Значения проекций скорости ($v_x, v_y$) и координат ($x, y$) тела в моменты времени $t$ от 0 до 5 с.
2. Построить траекторию движения тела и изобразить векторы скорости в указанные моменты времени на плоскости XY.
Решение:
Движение тела, брошенного под углом к горизонту, можно разложить на два независимых движения: равномерное движение вдоль горизонтальной оси X и равноускоренное движение вдоль вертикальной оси Y с ускорением $a_y = -g$.
Уравнения движения:
-
Для оси X (равномерное движение):
Проекция скорости: $v_x(t) = v_{0x}$
Координата: $x(t) = x_0 + v_{0x}t$
-
Для оси Y (равноускоренное движение):
Проекция скорости: $v_y(t) = v_{0y} - gt$
Координата: $y(t) = y_0 + v_{0y}t - \frac{gt^2}{2}$
Подставим известные значения ($x_0=0, y_0=0, v_{0x}=20, v_{0y}=30, g=10$):
- $v_x(t) = 20$ (м/с)
- $x(t) = 20t$ (м)
- $v_y(t) = 30 - 10t$ (м/с)
- $y(t) = 30t - 5t^2$ (м)
1. Заполнение таблицы
Вычислим требуемые величины для каждого момента времени от $t=0$ до $t=5$ с.
-
При $t=0$ с:
$v_x(0) = 20$ м/с
$v_y(0) = 30 - 10 \cdot 0 = 30$ м/с
$x(0) = 20 \cdot 0 = 0$ м
$y(0) = 30 \cdot 0 - 5 \cdot 0^2 = 0$ м
-
При $t=1$ с:
$v_x(1) = 20$ м/с
$v_y(1) = 30 - 10 \cdot 1 = 20$ м/с
$x(1) = 20 \cdot 1 = 20$ м
$y(1) = 30 \cdot 1 - 5 \cdot 1^2 = 30 - 5 = 25$ м
-
При $t=2$ с:
$v_x(2) = 20$ м/с
$v_y(2) = 30 - 10 \cdot 2 = 10$ м/с
$x(2) = 20 \cdot 2 = 40$ м
$y(2) = 30 \cdot 2 - 5 \cdot 2^2 = 60 - 20 = 40$ м
-
При $t=3$ с:
$v_x(3) = 20$ м/с
$v_y(3) = 30 - 10 \cdot 3 = 0$ м/с
$x(3) = 20 \cdot 3 = 60$ м
$y(3) = 30 \cdot 3 - 5 \cdot 3^2 = 90 - 45 = 45$ м (высшая точка траектории)
-
При $t=4$ с:
$v_x(4) = 20$ м/с
$v_y(4) = 30 - 10 \cdot 4 = -10$ м/с
$x(4) = 20 \cdot 4 = 80$ м
$y(4) = 30 \cdot 4 - 5 \cdot 4^2 = 120 - 80 = 40$ м
-
При $t=5$ с:
$v_x(5) = 20$ м/с
$v_y(5) = 30 - 10 \cdot 5 = -20$ м/с
$x(5) = 20 \cdot 5 = 100$ м
$y(5) = 30 \cdot 5 - 5 \cdot 5^2 = 150 - 125 = 25$ м
Сведем результаты в таблицу:
| Момент времени t, с | 0 | 1 | 2 | 3 | 4 | 5 |
| Проекция скорости тела на ось X, м/с | 20 | 20 | 20 | 20 | 20 | 20 |
| Проекция скорости тела на ось Y, м/с | 30 | 20 | 10 | 0 | -10 | -20 |
| Координата тела x, м | 0 | 20 | 40 | 60 | 80 | 100 |
| Координата тела y, м | 0 | 25 | 40 | 45 | 40 | 25 |
Ответ: Заполненная таблица представлена выше.
2. Построение графика траектории и векторов скорости
Используя вычисленные координаты ($x, y$), строим траекторию движения тела. В каждой точке, соответствующей моментам времени $t=0, 1, 2, 3, 4, 5$ с, строим вектор скорости $\vec{v}$, компонентами которого являются вычисленные значения $v_x$ и $v_y$. Вектор скорости всегда направлен по касательной к траектории.
Ответ: График траектории (синяя кривая) и векторов скорости (красные стрелки) в моменты времени $t = 0, 1, 2, 3, 4, 5$ с показан на рисунке выше.
Другие задания:
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