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Консультация № 199225
28.09.2020, 16:13
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Здравствуйте! У меня возникли сложности с таким вопросом:
Частица движется так, что ее радиус-вектор зависит от времени по закону r(t) = i·A(t/τ)3 + j·B(t/τ)4 + k·С, где A, B, С – постоянные величины, i, j, k – единичные орты в декартовой системе координат. Найдите тангенс угла, под которым будет направлена скорость v к оси x в момент времени t = 1 С, если τ = 1 с, А = 2 м, В = 3 м, С = 4 м.
Частица движется так, что ее радиус-вектор зависит от времени по закону r(t) = i·A(t/τ)3 + j·B(t/τ)4 + k·С, где A, B, С – постоянные величины, i, j, k – единичные орты в декартовой системе координат. Найдите тангенс угла, под которым будет направлена скорость v к оси x в момент времени t = 1 С, если τ = 1 с, А = 2 м, В = 3 м, С = 4 м.
Обсуждение
29.09.2020, 00:52
общий
это ответ
Здравствуйте, savelev.perm.bio!
Если позволите, я перепишу ваше уравнение в более мне привычный вид... Позволите?
Ну тогда вот так
r(t) = (3A/т)i *t + (4B/т)j*t + k·С
Тогда выражения в скобках - это скорости точки соответственно в проекциях вдоль осей х и y
vx=3A/т = 3*2м/1с = 6 м/с
vy=4B/т = 4*3м/1с = 12 м/с
Тангенс угла вектора скорости к оси х
tg[$945$]=vy/vx=12/6 = 2
Вроде всё.
Если позволите, я перепишу ваше уравнение в более мне привычный вид... Позволите?
Ну тогда вот так
r(t) = (3A/т)i *t + (4B/т)j*t + k·С
Тогда выражения в скобках - это скорости точки соответственно в проекциях вдоль осей х и y
vx=3A/т = 3*2м/1с = 6 м/с
vy=4B/т = 4*3м/1с = 12 м/с
Тангенс угла вектора скорости к оси х
tg[$945$]=vy/vx=12/6 = 2
Вроде всё.
Об авторе:
С уважением
shvetski
С уважением
shvetski
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