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Задать вопрос экспертам

Консультация № 201998

27.12.2021, 23:06

0.00 руб.

0 1 1

Образование

Здравствуйте! Прошу помощи в следующем вопросе:
Камень, брошенный вертикально вверх пролетел, двигаясь в одном направлении, 8 м за первые 0,4 с полета.
Найдите скорость камня на высоте 6,5 м. Ускорение свободного падения 10 м/с^2. Сопротивление воздуха пренебрежимо мало. Ответ приведите в [м/с].

Обсуждение

давно

Посетитель
405239
95

30.12.2021, 13:35

общий

это ответ

Здравствуйте! Предлагаю следующее решение:
Дано: t = 0.4 с, h = 8 м, g = 10 м/с², H = 6.5 м.
Найти: v - ?
Решение:
Введем вертикальную ось y, направлена вверх, начало координат совпадает с уровнем точки броска. Пусть v_0y - проекция начальной скорости на эту ось.
По формуле "без конечной скорости" для равноускоренного движения (y = y₀ + v_0yt + a_yt² / 2): h = 0 + v_0yt - gt²/2 следовательно, v_0y = (h + gt²/2) / t = (2h + gt²) / 2t.
По формуле "без времени" для равноускоренного движения (y = y₀ + (v_y² - v_0y²) / (2a_y) ): H = 0 + (v_y² - v_0y²) / (2g) следовательно

.
Поскольку движение только вдоль оси y, искомая величина скорости v=|v_y| [$8776$] 18.81 м/с
Ответ: v [$8776$] 18.81 м/с

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