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Номер 8, страница 441 - гдз по физике 10 класс учебник Касьянов
Авторы: Касьянов В. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2021 - 2026
Уровень обучения: углублённый
Цвет обложки: белый самолет и молнии изображены
ISBN: 978-5-09-103621-3
Популярные ГДЗ в 10 классе
Лабораторные работы. 2. Изучение движения тела, брошенного горизонтально. Задание 2 - номер 8, страница 441.
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" => 1390556 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-8" "field_display_title" => "8" "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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "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 {#1080 #items: array:1 [ 0 => App\Models\Book {#1048 #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" => 7000 "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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #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" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #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 {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #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 {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #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" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "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 {#1057 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => 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:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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 {#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: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 {#1064 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => 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" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "field_translit" => "uglublennyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #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" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 7000 "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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053} "field_author" => Illuminate\Database\Eloquent\Collection {#1055} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1057} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1058} "field_country" => Illuminate\Database\Eloquent\Collection {#1060} "field_city" => Illuminate\Database\Eloquent\Collection {#1062} "field_series" => Illuminate\Database\Eloquent\Collection {#1064} "field_umk" => Illuminate\Database\Eloquent\Collection {#1065} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1066} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #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 {#1078 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "426" "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 {#1080} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1078} ] #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 {#1108 #items: array:3 [ 0 => App\Models\Branch {#1118 #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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "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 {#1120 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1119} "field_page_start" => "426" "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 {#1120} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1121} ] #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 {#1122 #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" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "438" "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 {#1124 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1123} "field_page_start" => "438" "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 {#1124} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1125} ] #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 {#1126 #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" => 1389656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 2" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "440" "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 {#1128 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Branch {#1136 #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" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "438" "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 {#1139 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Изучение движения тела, брошенного горизонтально" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1138} "field_page_start" => "438" "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 {#1139} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140} ] #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" => 1389656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 2" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127} "field_page_start" => "440" "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 {#1128} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137} ] #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 {#1100 #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" => 1640905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1098 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1097 #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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1097} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095} "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" => "1390556" "type" => "task" ] "text" => "<p><strong>8.</strong> Запишите значение дальности полёта с учётом абсолютной погрешности измерения:</p><p>$$l = l_{\text{cp}} \pm \Delta l.$$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1673" "height" => 281 "path" => "/media/fizika_10/kasyanov-u/0-lab02-2/8-1.webp?ts=1757958219" ] ] ] #original: array:7 [ "id" => 1640905 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1390556" "type" => "task" ] "text" => "<p><strong>8.</strong> Запишите значение дальности полёта с учётом абсолютной погрешности измерения:</p><p>$$l = l_{\text{cp}} \pm \Delta l.$$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1673" "height" => 281 "path" => "/media/fizika_10/kasyanov-u/0-lab02-2/8-1.webp?ts=1757958219" ] ] ] #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 {#1093 #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" => 1693568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Edition {#1092 #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" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087} "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" => "1390556" "type" => "task" ] "text" => "<p><strong>8.</strong> Запишите значение дальности полёта с учётом абсолютной погрешности измерения:</p><p>Чтобы записать значение дальности полёта с учётом абсолютной погрешности, необходимо иметь результаты нескольких измерений этой дальности. Формула для записи результата имеет вид:</p><p>$l = l_{ср} \pm \Delta l$</p><p>где:<br>$l_{ср}$ – среднее арифметическое значение измеренной дальности полёта,<br>$\Delta l$ – абсолютная погрешность измерения.</p><p>Поскольку в задании не приведены результаты измерений, для демонстрации метода решения приведём пример расчёта на гипотетических данных.</p><p><strong>Дано:</strong></p><p>Предположим, было проведено 5 измерений дальности полёта ($n=5$) с помощью измерительной ленты с ценой деления 1 см. Получены следующие результаты:<br>$l_1 = 85 \text{ см}$<br>$l_2 = 87 \text{ см}$<br>$l_3 = 84 \text{ см}$<br>$l_4 = 86 \text{ см}$<br>$l_5 = 85 \text{ см}$<br>Цена деления прибора: $c = 1 \text{ см}$.</p><p>$l_1 = 0.85 \text{ м}$<br>$l_2 = 0.87 \text{ м}$<br>$l_3 = 0.84 \text{ м}$<br>$l_4 = 0.86 \text{ м}$<br>$l_5 = 0.85 \text{ м}$<br>$c = 0.01 \text{ м}$.</p><p><strong>Найти:</strong></p><p>$l$ - значение дальности полёта с учётом абсолютной погрешности.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Найдём среднее значение дальности полёта ($l_{ср}$):</p><p>$l_{ср} = \frac{l_1 + l_2 + l_3 + l_4 + l_5}{n} = \frac{0.85 + 0.87 + 0.84 + 0.86 + 0.85}{5} = \frac{4.27}{5} = 0.854 \text{ м}$.</p><p><strong>2.</strong> Рассчитаем абсолютную погрешность $\Delta l$. Она складывается из случайной погрешности ($\Delta l_{сл}$), обусловленной разбросом результатов, и приборной погрешности ($\Delta l_{пр}$), связанной с точностью измерительного инструмента.</p><p>а) Случайную погрешность для небольшого числа измерений можно оценить как половину размаха (разницы между максимальным и минимальным значениями):</p><p>$l_{max} = 0.87 \text{ м}$<br>$l_{min} = 0.84 \text{ м}$<br>$\Delta l_{сл} = \frac{l_{max} - l_{min}}{2} = \frac{0.87 - 0.84}{2} = \frac{0.03}{2} = 0.015 \text{ м}$.</p><p>б) Приборная погрешность обычно принимается равной половине цены деления измерительного прибора. Цена деления $c = 0.01$ м, следовательно:</p><p>$\Delta l_{пр} = \frac{c}{2} = \frac{0.01}{2} = 0.005 \text{ м}$.</p><p>в) Полная абсолютная погрешность $\Delta l$ находится как сумма случайной и приборной погрешностей:</p><p>$\Delta l = \Delta l_{сл} + \Delta l_{пр} = 0.015 + 0.005 = 0.020 \text{ м}$.</p><p><strong>3.</strong> Округлим результаты в соответствии с правилами. Абсолютную погрешность $\Delta l$ принято округлять до одной значащей цифры. В нашем случае $\Delta l = 0.02$ м, что уже соответствует этому правилу.</p><p><strong>4.</strong> Среднее значение $l_{ср}$ округляется до того же десятичного разряда, что и погрешность. Погрешность $\Delta l$ определена до сотых долей метра, значит, и $l_{ср}$ нужно округлить до сотых.</p><p>$l_{ср} = 0.854 \text{ м} \approx 0.85 \text{ м}$.</p><p><strong>5.</strong> Запишем окончательный результат в виде $l = l_{ср} \pm \Delta l$.</p><p>$l = (0.85 \pm 0.02) \text{ м}$.</p><p>Это означает, что истинное значение дальности полёта с высокой вероятностью находится в интервале от $0.83$ м до $0.87$ м.</p><p><strong>Ответ:</strong> Поскольку данные для расчета отсутствуют в условии, окончательный ответ можно записать только в общем виде $l = l_{ср} \pm \Delta l$. На основе приведённого выше примера расчёта: $l = (0.85 \pm 0.02) \text{ м}$.</p>" ] #original: array:6 [ "id" => 1693568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084} "task" => array:2 [ "refs" => "1390556" "type" => "task" ] "text" => "<p><strong>8.</strong> Запишите значение дальности полёта с учётом абсолютной погрешности измерения:</p><p>Чтобы записать значение дальности полёта с учётом абсолютной погрешности, необходимо иметь результаты нескольких измерений этой дальности. Формула для записи результата имеет вид:</p><p>$l = l_{ср} \pm \Delta l$</p><p>где:<br>$l_{ср}$ – среднее арифметическое значение измеренной дальности полёта,<br>$\Delta l$ – абсолютная погрешность измерения.</p><p>Поскольку в задании не приведены результаты измерений, для демонстрации метода решения приведём пример расчёта на гипотетических данных.</p><p><strong>Дано:</strong></p><p>Предположим, было проведено 5 измерений дальности полёта ($n=5$) с помощью измерительной ленты с ценой деления 1 см. Получены следующие результаты:<br>$l_1 = 85 \text{ см}$<br>$l_2 = 87 \text{ см}$<br>$l_3 = 84 \text{ см}$<br>$l_4 = 86 \text{ см}$<br>$l_5 = 85 \text{ см}$<br>Цена деления прибора: $c = 1 \text{ см}$.</p><p>$l_1 = 0.85 \text{ м}$<br>$l_2 = 0.87 \text{ м}$<br>$l_3 = 0.84 \text{ м}$<br>$l_4 = 0.86 \text{ м}$<br>$l_5 = 0.85 \text{ м}$<br>$c = 0.01 \text{ м}$.</p><p><strong>Найти:</strong></p><p>$l$ - значение дальности полёта с учётом абсолютной погрешности.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Найдём среднее значение дальности полёта ($l_{ср}$):</p><p>$l_{ср} = \frac{l_1 + l_2 + l_3 + l_4 + l_5}{n} = \frac{0.85 + 0.87 + 0.84 + 0.86 + 0.85}{5} = \frac{4.27}{5} = 0.854 \text{ м}$.</p><p><strong>2.</strong> Рассчитаем абсолютную погрешность $\Delta l$. Она складывается из случайной погрешности ($\Delta l_{сл}$), обусловленной разбросом результатов, и приборной погрешности ($\Delta l_{пр}$), связанной с точностью измерительного инструмента.</p><p>а) Случайную погрешность для небольшого числа измерений можно оценить как половину размаха (разницы между максимальным и минимальным значениями):</p><p>$l_{max} = 0.87 \text{ м}$<br>$l_{min} = 0.84 \text{ м}$<br>$\Delta l_{сл} = \frac{l_{max} - l_{min}}{2} = \frac{0.87 - 0.84}{2} = \frac{0.03}{2} = 0.015 \text{ м}$.</p><p>б) Приборная погрешность обычно принимается равной половине цены деления измерительного прибора. Цена деления $c = 0.01$ м, следовательно:</p><p>$\Delta l_{пр} = \frac{c}{2} = \frac{0.01}{2} = 0.005 \text{ м}$.</p><p>в) Полная абсолютная погрешность $\Delta l$ находится как сумма случайной и приборной погрешностей:</p><p>$\Delta l = \Delta l_{сл} + \Delta l_{пр} = 0.015 + 0.005 = 0.020 \text{ м}$.</p><p><strong>3.</strong> Округлим результаты в соответствии с правилами. Абсолютную погрешность $\Delta l$ принято округлять до одной значащей цифры. В нашем случае $\Delta l = 0.02$ м, что уже соответствует этому правилу.</p><p><strong>4.</strong> Среднее значение $l_{ср}$ округляется до того же десятичного разряда, что и погрешность. Погрешность $\Delta l$ определена до сотых долей метра, значит, и $l_{ср}$ нужно округлить до сотых.</p><p>$l_{ср} = 0.854 \text{ м} \approx 0.85 \text{ м}$.</p><p><strong>5.</strong> Запишем окончательный результат в виде $l = l_{ср} \pm \Delta l$.</p><p>$l = (0.85 \pm 0.02) \text{ м}$.</p><p>Это означает, что истинное значение дальности полёта с высокой вероятностью находится в интервале от $0.83$ м до $0.87$ м.</p><p><strong>Ответ:</strong> Поскольку данные для расчета отсутствуют в условии, окончательный ответ можно записать только в общем виде $l = l_{ср} \pm \Delta l$. На основе приведённого выше примера расчёта: $l = (0.85 \pm 0.02) \text{ м}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390557" "type" => "task" ] "previous" => array:2 [ "refs" => "1390555" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1105 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1391089 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-441" "field_display_title" => "441" "field_folder" => "1" "field_image_name" => "441" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Element {#1114 #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" => 1641589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1641589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112} "book_page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1391090" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391088" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:7 [ 0 => App\Models\Task {#1214 #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" => 1390554 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1215 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1216 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390555" "type" => "task" ] "previous" => array:2 [ "refs" => "1390553" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390554 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1215} "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 {#1216} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1217} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1218} "content" => Illuminate\Database\Eloquent\Collection {#1220} "next" => array:2 [ "refs" => "1390555" "type" => "task" ] "previous" => array:2 [ "refs" => "1390553" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1226} "page" => array:2 [ "refs" => "1391089" "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 => "*" ] } 1 => App\Models\Task {#1221 #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" => 1390555 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1228 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390556" "type" => "task" ] "previous" => array:2 [ "refs" => "1390554" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390555 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1219} "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 {#1228} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1224} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1222} "content" => Illuminate\Database\Eloquent\Collection {#1223} "next" => array:2 [ "refs" => "1390556" "type" => "task" ] "previous" => array:2 [ "refs" => "1390554" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1238} "page" => array:2 [ "refs" => "1391089" "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 => "*" ] } 2 => App\Models\Task {#1233 #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" => 1390556 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1240 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390557" "type" => "task" ] "previous" => array:2 [ "refs" => "1390555" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390556 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1225} "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 {#1240} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1236} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1234} "content" => Illuminate\Database\Eloquent\Collection {#1237} "next" => array:2 [ "refs" => "1390557" "type" => "task" ] "previous" => array:2 [ "refs" => "1390555" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1235} "page" => array:2 [ "refs" => "1391089" "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 => "*" ] } 3 => App\Models\Task {#1245 #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" => 1390557 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1247 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390558" "type" => "task" ] "previous" => array:2 [ "refs" => "1390556" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390557 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246} "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 {#1247} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1248} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249} "content" => Illuminate\Database\Eloquent\Collection {#1251} "next" => array:2 [ "refs" => "1390558" "type" => "task" ] "previous" => array:2 [ "refs" => "1390556" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1257} "page" => array:2 [ "refs" => "1391089" "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 => App\Models\Task {#1252 #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" => 1390558 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1259 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390559" "type" => "task" ] "previous" => array:2 [ "refs" => "1390557" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391089" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390558 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1250} "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 {#1259} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1253} "content" => Illuminate\Database\Eloquent\Collection {#1254} "next" => array:2 [ "refs" => "1390559" "type" => "task" ] "previous" => array:2 [ "refs" => "1390557" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1269} "page" => array:2 [ "refs" => "1391089" "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 => "*" ] } 5 => App\Models\Task {#1264 #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" => 1390559 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1271 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390560" "type" => "task" ] "previous" => array:2 [ "refs" => "1390558" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391089" …1 ] ] #original: array:24 [ "id" => 1390559 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256} "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 {#1271} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265} "content" => Illuminate\Database\Eloquent\Collection {#1266} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1281} "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 => "*" ] } 6 => App\Models\Task {#1276 #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" => 1390560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1268 …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 {#1283 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1279 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 …2} "content" => Illuminate\Database\Eloquent\Collection {#1278 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1293 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1268 …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 {#1283 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1279 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 …2} "content" => Illuminate\Database\Eloquent\Collection {#1278 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1293 …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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1391089 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-441" "field_display_title" => "441" "field_folder" => "1" "field_image_name" => "441" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1085} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1083} "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 {#1081} "content" => Illuminate\Database\Eloquent\Collection {#1116} "next" => array:2 [ "refs" => "1391090" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391088" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1200} ] #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" => 1390556 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "441" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab02-2-8" "field_display_title" => "8" "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 {#1108} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1390557" "type" => "task" ] "previous" => array:2 [ "refs" => "1390555" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103} "page" => array:2 [ "refs" => "1391089" "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 => "*" ] }
№8 (с. 441)
Условие. №8 (с. 441)
скриншот условия
8. Запишите значение дальности полёта с учётом абсолютной погрешности измерения:
$$l = l_{\text{cp}} \pm \Delta l.$$
Решение. №8 (с. 441)
8. Запишите значение дальности полёта с учётом абсолютной погрешности измерения:
Чтобы записать значение дальности полёта с учётом абсолютной погрешности, необходимо иметь результаты нескольких измерений этой дальности. Формула для записи результата имеет вид:
$l = l_{ср} \pm \Delta l$
где:
$l_{ср}$ – среднее арифметическое значение измеренной дальности полёта,
$\Delta l$ – абсолютная погрешность измерения.
Поскольку в задании не приведены результаты измерений, для демонстрации метода решения приведём пример расчёта на гипотетических данных.
Дано:
Предположим, было проведено 5 измерений дальности полёта ($n=5$) с помощью измерительной ленты с ценой деления 1 см. Получены следующие результаты:
$l_1 = 85 \text{ см}$
$l_2 = 87 \text{ см}$
$l_3 = 84 \text{ см}$
$l_4 = 86 \text{ см}$
$l_5 = 85 \text{ см}$
Цена деления прибора: $c = 1 \text{ см}$.
$l_1 = 0.85 \text{ м}$
$l_2 = 0.87 \text{ м}$
$l_3 = 0.84 \text{ м}$
$l_4 = 0.86 \text{ м}$
$l_5 = 0.85 \text{ м}$
$c = 0.01 \text{ м}$.
Найти:
$l$ - значение дальности полёта с учётом абсолютной погрешности.
Решение:
1. Найдём среднее значение дальности полёта ($l_{ср}$):
$l_{ср} = \frac{l_1 + l_2 + l_3 + l_4 + l_5}{n} = \frac{0.85 + 0.87 + 0.84 + 0.86 + 0.85}{5} = \frac{4.27}{5} = 0.854 \text{ м}$.
2. Рассчитаем абсолютную погрешность $\Delta l$. Она складывается из случайной погрешности ($\Delta l_{сл}$), обусловленной разбросом результатов, и приборной погрешности ($\Delta l_{пр}$), связанной с точностью измерительного инструмента.
а) Случайную погрешность для небольшого числа измерений можно оценить как половину размаха (разницы между максимальным и минимальным значениями):
$l_{max} = 0.87 \text{ м}$
$l_{min} = 0.84 \text{ м}$
$\Delta l_{сл} = \frac{l_{max} - l_{min}}{2} = \frac{0.87 - 0.84}{2} = \frac{0.03}{2} = 0.015 \text{ м}$.
б) Приборная погрешность обычно принимается равной половине цены деления измерительного прибора. Цена деления $c = 0.01$ м, следовательно:
$\Delta l_{пр} = \frac{c}{2} = \frac{0.01}{2} = 0.005 \text{ м}$.
в) Полная абсолютная погрешность $\Delta l$ находится как сумма случайной и приборной погрешностей:
$\Delta l = \Delta l_{сл} + \Delta l_{пр} = 0.015 + 0.005 = 0.020 \text{ м}$.
3. Округлим результаты в соответствии с правилами. Абсолютную погрешность $\Delta l$ принято округлять до одной значащей цифры. В нашем случае $\Delta l = 0.02$ м, что уже соответствует этому правилу.
4. Среднее значение $l_{ср}$ округляется до того же десятичного разряда, что и погрешность. Погрешность $\Delta l$ определена до сотых долей метра, значит, и $l_{ср}$ нужно округлить до сотых.
$l_{ср} = 0.854 \text{ м} \approx 0.85 \text{ м}$.
5. Запишем окончательный результат в виде $l = l_{ср} \pm \Delta l$.
$l = (0.85 \pm 0.02) \text{ м}$.
Это означает, что истинное значение дальности полёта с высокой вероятностью находится в интервале от $0.83$ м до $0.87$ м.
Ответ: Поскольку данные для расчета отсутствуют в условии, окончательный ответ можно записать только в общем виде $l = l_{ср} \pm \Delta l$. На основе приведённого выше примера расчёта: $l = (0.85 \pm 0.02) \text{ м}$.
Другие задания:
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