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Консультация № 199656
19.11.2020, 11:06
0.00 руб.
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Радиус-вектор частицы зависит от времени по закону
(на фото)
Через сколько секунд скорость частицы окажется перпендикуляр-ной оси y, если т=1 с, А = В = 1 м, ω=п/2 рад/с.
Радиус-вектор частицы зависит от времени по закону
(на фото)
Через сколько секунд скорость частицы окажется перпендикуляр-ной оси y, если т=1 с, А = В = 1 м, ω=п/2 рад/с.
Прикрепленные файлы:
Обсуждение
24.11.2020, 05:55
общий
это ответ
Здравствуйте, Дмитрий!
Подставляя исходные данные в выражение для радиус-вектора, получаем
то есть x = t[sup]3[/sup], y = t[sup]4[/sup] - t[sup]6[/sup], z = sin [$960$]t/2. Скорость является производной по времени от радиус-вектора:
то есть v[sub]x[/sub] = 3t[sup]2[/sup], v[sub]y[/sub] = 4t[sup]3[/sup] - 6t[sup]5[/sup], v[sub]z[/sub] = [$960$]/2 cos [$960$]t/2. Если в момент времени t скорость частицы перпендикулярна оси y, то v[sub]y[/sub](t) = 0, то есть 4t[sup]3[/sup] - 6t[sup]5[/sup] = 0, что возможно при t = 0 и при t = [$8730$]2/3 [$8776$] 0.816 c.
Подставляя исходные данные в выражение для радиус-вектора, получаем
то есть x = t[sup]3[/sup], y = t[sup]4[/sup] - t[sup]6[/sup], z = sin [$960$]t/2. Скорость является производной по времени от радиус-вектора:
то есть v[sub]x[/sub] = 3t[sup]2[/sup], v[sub]y[/sub] = 4t[sup]3[/sup] - 6t[sup]5[/sup], v[sub]z[/sub] = [$960$]/2 cos [$960$]t/2. Если в момент времени t скорость частицы перпендикулярна оси y, то v[sub]y[/sub](t) = 0, то есть 4t[sup]3[/sup] - 6t[sup]5[/sup] = 0, что возможно при t = 0 и при t = [$8730$]2/3 [$8776$] 0.816 c.
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