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Задать вопрос экспертам

Консультация № 199758

02.12.2020, 12:51

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Образование

Здравствуйте! Прошу помощи в следующем вопросе: Из маленькой игрушечной катапульты под углом 45∘ к горизонту запускают тяжёлый шарик со скоростью 6 м/с. На расстоянии 1,8 м от катапульты устанавливают небольшую мишень на подставке. Какой высоты должна быть подставка, чтобы шарик попал в мишень? Ответ запишите в метрах, округлив до десятых. Сопротивлением воздуха пренебречь, ускорение свободного падения считать равным 10 м/с2.

Обсуждение

давно

Посетитель
226425
1567

06.12.2020, 13:37

общий

это ответ

Здравствуйте, mathru10@gmail.com!
Дано:
[$945$]₀=45[$186$]
v₀=6 м/с
х₁=1,8 м
g=10 м/с²
Найти:
y₁
Решение:
1. Движение шарика вдоль оси х (по горизонтали) - равномерное, согласно уравнению
x=v_0xt (1)
2. Движение шарика вдоль оси у (по высоте) - равноускоренное, согласно уравнению
y=v_0yt-gt²/2 (2)
3. Проекции скорости:
- на ось х
v_0x=v₀*cos[$945$] (3)
- на ось у
v_0y=v₀*sin[$945$] (4)
4. Шарик попадает в мишень на высоте y=y₁ ровно в тот самый момент времени t₁, когда долетает до координаты x=x₁.
5. Найдем момент времени t₁ из уравнения (1)
t₁=x₁/v₀cos[$945$] (5)
6. Подставим результат (5) в уравнение (2). Получим
y₁=x₁*tg[$945$]-(1/2)*g*(x₁/v₀cos[$945$])² (6)
Подставляем данные в условии значения в выражение (6) и получаем
y₁[$8776$]0,4 м

Об авторе:
С уважением
shvetski

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