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Консультация № 191423
03.10.2017, 15:22
0.00 руб.
0
3
2
Здравствуйте! У меня возникли сложности с таким вопросом:
Свободно падающее тело в последние 2 с своего движения проходит ¾ всего пути. Определите высоту, с которой падало тело без начальной скорости.
Свободно падающее тело в последние 2 с своего движения проходит ¾ всего пути. Определите высоту, с которой падало тело без начальной скорости.
Обсуждение
03.10.2017, 17:35
общий
это ответ
Здравствуйте, karmaev.1995!
Уравнение движения тела с постоянным ускорением a в общем случае имеет вид
где S[sub]0[/sub] и V[sub]0[/sub] - начальные положение и скорость. Если тело падает с высоты h без начальной скорости, то S[sub]0[/sub] = h, V[sub]0[/sub] = 0, a = -g (ускорение свободного падения) и для момента t, в который S = 0, имеем
то есть высота падения пропорциональна квадрату времени. Отсюда следует, что за первую половину времени движения тело проходит четверть пути, а за вторую - три четверти. В данном случае эта половина составляет 2 с, следовательно, тело падало в течение 4 с, и высота падения равна
если принять g [$8776$] 10 м/с[sup]2[/sup].
Уравнение движения тела с постоянным ускорением a в общем случае имеет вид
где S[sub]0[/sub] и V[sub]0[/sub] - начальные положение и скорость. Если тело падает с высоты h без начальной скорости, то S[sub]0[/sub] = h, V[sub]0[/sub] = 0, a = -g (ускорение свободного падения) и для момента t, в который S = 0, имеем
то есть высота падения пропорциональна квадрату времени. Отсюда следует, что за первую половину времени движения тело проходит четверть пути, а за вторую - три четверти. В данном случае эта половина составляет 2 с, следовательно, тело падало в течение 4 с, и высота падения равна
если принять g [$8776$] 10 м/с[sup]2[/sup].
03.10.2017, 18:19
общий
это ответ
Здравствуйте, karmaev.1995!
Пусть
- время, затраченное телом на падение с высоты 
За время, равное 
с, тело преодолеет высоту, равную 
Значит,
Разделив почленно первое уравнение на второе, получим
откуда
с или 
с.
Но, согласно условию задачи, должно быть больше двух секунд, поэтому с, и
(м).
Пусть
- время, затраченное телом на падение с высоты За время, равное с, тело преодолеет высоту, равную Значит,Разделив почленно первое уравнение на второе, получим
откуда
с или с.Но, согласно условию задачи,
должно быть больше двух секунд, поэтому с, и (м).
4
Об авторе:
Facta loquuntur.
Facta loquuntur.
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