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Здравствуйте! Прошу помощи в следующем вопросе: Ракета, запущенная вертикально, достигла максимальной высоты H =192 км. Во время работы двигателя ускорение ракеты a = 2 м/с2. Сколько времени t работал двигатель?
Вы забываете, что по мере удаления от поверхности Земли ускорение свободного падения уменьшается? Если на поверхности Земли оно составляет то на высоте над поверхностью Земли -- где -- радиус Земли. Кроме того, как я сообщил Вам, Цитата: Гордиенко Андрей Владимирович
Реактивное движение предполагает изменение массы ракеты.
По-моему, главный подвох в этой задаче состоит в том, что ракета не движется с постоянным ускорением. Как я понимаю, ракета то ускоряется силой тяги, то замедляется силой земного притяжения, которая к тому же по величине непостоянна.
По-моему, если бы высота, на которую поднялась ракета, составляла не 192 километра, а 192 метра, то изменением ускорения свободного падения можно было бы пренебречь. Тогда задачу можно было бы решить.
Я предполагаю, что первоисточник этой задачи находится здесь. Вами предложена формулировка только первой части задачи. Тем не менее, задача имеет "олимпиадный" уровень и предлагать её экспертам для решения некорректно, тем более, что профессионалы-знатоки физики почти не отвечают на вопросы консультаций. Прошу Вас иметь это в виду впредь!
В документе, ссылку на который я привёл, имеется ответ к этой задаче: время работы двигателя составляет
(с).
При таком выражении ответа (с точностью до двух десятичных знаков), действительно, можно пренебречь изменением ускорения свободного падения в зависимости от высоты подъёма ракеты. Ответ же, который дан в документе, я считаю неверно записанным с точки зрения вычислительной математики.
Попробую объяснить Вам, как можно получить нужный ответ. Предположим, что в течение промежутка времени ракета двигалась с включенным двигателем, а в течение промежутка времени -- с выключенным двигателем. Обозначим -- начальная скорость ракеты, -- скорость ракеты в конце первого промежутка времени, -- скорость ракеты в конце второго промежутка времени (на высоте ), -- высота, на которую поднялась ракета в конце первого промежутка времени, -- масса ракеты при выключенном двигателе (она не изменяется, потому что топливо не расходуется).
Примем, что потенциальная энергия ракеты на поверхности Земли равна нулю. Тогда её потенциальная энергия на высоте составляет (считаем ускорение свободного падения постоянным)
а на высоте --
для кинетической энергии имеем соответственно
и
в соответствии с законом сохранения механической энергии,
Учитывая, что
из формулы (1) получим
Литература Аксенович Л. А., Ракина Н. Н., Фарино К. С. Физика в средней школе. -- Минск: Адукацыя i выхаванне, 2004. -- 720 с.
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Форма ответа
Отправка постов/ответов доступна только зарегистрированным и подтвержденным пользователям.
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Откуда Вы взяли эту задачу?
то на высоте 
над поверхностью Земли -- 
где 
-- радиус Земли. Кроме того, как я сообщил Вам,
Гордиенко Андрей Владимирович 
(с).
ракета двигалась с включенным двигателем, а в течение промежутка времени 
-- с выключенным двигателем. Обозначим 
-- начальная скорость ракеты, 
-- скорость ракеты в конце первого промежутка времени, 
-- скорость ракеты в конце второго промежутка времени (на высоте 
), 
-- масса ракеты при выключенном двигателе (она не изменяется, потому что топливо не расходуется).
и 
