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Консультация № 109108

12.11.2007, 19:32

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Образование

Уважаемые знатоки помогите пожалуйста !С поверхности земли вертикально вверх пущена ракета со скоростью U=5 км/с.На какую высоту она поднимется?

Обсуждение

Неизвестный

17.11.2007, 11:54

общий

это ответ

<font color=blue><b>!!!</b></font>
Здравствуйте, Карачев Сергей Александрович!

Уважаемые знатоки помогите пожалуйста !С поверхности земли вертикально вверх пущена ракета со скоростью U=5 км/с.На какую высоту она поднимется?

Если бы ракета двигалась с постоянным ускорением g = 10, то ей потребовалось бы U/g = 500 секунд, чтобы остановиться. При этом она бы пролетела U<sup>2</sup>/(2*g) = 1250 км, что сравнимо с радиусом Земли 6400 км.
Для учёта изменения ускорения с высотой мы должны прибегнуть к использованию закона всемироного тяготения, согласно которому изменение потенциальной энергии равно G*m*M*(1/R - 1/(R+h)).
Таким образом, mU<sup>2</sup>/2 = G*m*M*(1/R - 1/(R+h)).
Откуда h = 1/(1/R - <s>m</s>U<sup>2</sup>/(2*G*M)) - R.
Для нахождения G*M учтём, что ускорение свободного падения вблизи Земли g = G*M/R<sup>2</sup>, т.е. G*M = g*R<sup>2</sup>.
Подставим и получим h = 1/(1/R - <s>m</s>U<sup>2</sup>/(2*g*R<sup>2</sup>)) - R = 2*g*R<sup>2</sup>/(2*g*R - <s>m</s>U<sup>2</sup>) - R = <s>m</s>U<sup>2</sup>R/(2*g*R - <s>m</s>U<sup>2</sup>).
<p><fieldset style=‘background-color:#EFEFEF; width:80%; border:blue 1px solid; padding:10px;‘ class=fieldset><font color=blue><i>См. минифорум</i>
-----
</font><font color=#777777 size=1><b>• Отредактировал: <a href=/info/user/8 target=_blank>Alexandre V. Tchamaev</a></b> (*Мастер-Эксперт)
<b>• Дата редактирования:</b> 22.11.2007, 04:19</font></fieldset>

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