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Задать вопрос экспертам

Консультация № 177436

24.03.2010, 14:24

43.65 руб.

0 1 1

Образование

Под каким углом к горизонту следует направить ствол орудия, чтобы поразить цель, находящуюся на расстоянии 6 км от него? Начальная скорость снаряда 600 м/с.

Обсуждение

Неизвестный

24.03.2010, 15:53

общий

это ответ

Здравствуйте, Эдик В.
Расстояние S, которое пролетает снаряд зависит от горизонтальной составляющей начальной скорости V и времени полёта t: S = t*V*cos(a) = 6км, где a - угол к горизонту.
Скорость зависит в свою очередь от вертикальной составляющей: t = 2*V*sin(a)/g.
S = 2*V²*cos(a)*sin(a)/g
Выразим отсюда угол а, пользуясь отношением cos(a)*sin(a) = sin(2*a)/2:
sin(2*a) = S*g/V²
a = arcsin(S*g/V²)/2
Подставляем значения:
a = arcsin(6000*9.8/600²)/2 = arcsin(0.163)/2
Угол a имеет диапазон значений от 0 до pi/2, поэтому нам нужны значения arcsin в интервале (0, pi). Есть два таких значения: 9.4[$186$] и 180[$186$] - 9.4[$186$] = 170.6[$186$], соответственно a тоже имеет два значения: 9.4[$186$]/2 = 4.7[$186$] и 170.6[$186$]/2 = 85.3[$186$]
Ответ: 4.7[$186$] и 85.3[$186$]

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