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Консультация № 104220
04.10.2007, 00:33
0.00 руб.
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1
Срочно помогите с решением следующих задач!
1) аэростат начинает подъем с земли с постоянным ускорением а=0,5 м/с^2. Когда аэростат поднялся на высоту р=20 м , из него выпал предмет. На какой максимальной высоте лн побывает? Сопротивлением воздуха пренебречь.
2) Под каким углом a к горизонту нужно направлять струю воды, чтобы высота ее подъема превышала дальность полета?
1) аэростат начинает подъем с земли с постоянным ускорением а=0,5 м/с^2. Когда аэростат поднялся на высоту р=20 м , из него выпал предмет. На какой максимальной высоте лн побывает? Сопротивлением воздуха пренебречь.
2) Под каким углом a к горизонту нужно направлять струю воды, чтобы высота ее подъема превышала дальность полета?
Обсуждение
04.10.2007, 10:44
общий
это ответ
Здравствуйте, Timon!
2) Начальная скорость струи V, её вертикальная составляющая Vв = V*SIN(α) (1), горизонтальная Vг = V*COS(α) (2). Вертикальная скорость частиц воды равномерно уменьшается до нуля, поэтому средняя её величина равна: Vвср = Vв/2. На подъём до высоты h уходит время tп = h/Vвср = h/(Vв/2) = 2*(h/Vв). Столько же уходит на возврат к исходному уровню, итого общее время "полёта" струи tо = 4*(h/Vв) = 4*h/(V*SIN(α)) (3). Горизонтальная составляющая в "полёте" остаётся постоянной, поэтому дальность "полета" L = Vг*tо = tо*V*COS(α) (4), или, подставив значение tо из (3): L = 4*h*COS(α)/SIN(α) = 4*h*CTG(α) (5). Если h >= L, то TG(α) >= 4, откуда α >= 76°.
2) Начальная скорость струи V, её вертикальная составляющая Vв = V*SIN(α) (1), горизонтальная Vг = V*COS(α) (2). Вертикальная скорость частиц воды равномерно уменьшается до нуля, поэтому средняя её величина равна: Vвср = Vв/2. На подъём до высоты h уходит время tп = h/Vвср = h/(Vв/2) = 2*(h/Vв). Столько же уходит на возврат к исходному уровню, итого общее время "полёта" струи tо = 4*(h/Vв) = 4*h/(V*SIN(α)) (3). Горизонтальная составляющая в "полёте" остаётся постоянной, поэтому дальность "полета" L = Vг*tо = tо*V*COS(α) (4), или, подставив значение tо из (3): L = 4*h*COS(α)/SIN(α) = 4*h*CTG(α) (5). Если h >= L, то TG(α) >= 4, откуда α >= 76°.
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