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Консультация № 199263
06.10.2020, 17:42
0.00 руб.
0
3
1
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.
Заранее спасибо за помощь.
Обсуждение
07.10.2020, 00:14
общий
это ответ
Здравствуйте, savelev.perm.bio!
что-то до боли знакомые задачи...
Дано:
r(t) = i•A(t/[$964$])3 + j•B(t/[$964$])4 + k•С
[$964$]=1 с, А=2 м, В=3 м, С=4 м
t1 = 1 с
[$945$]=[$8736$][$8594$]v;[$8594$]x
Найти:
tg[$945$]1
Решение:
Возьмем производную от уравнения радиус вектора по времени. Получим уравнение скорости:
v(t)=r'(t)=i*(3A/т3)*t2+j*(4B/т4)*t3 (*)
В выражении (*) первое слагаемое является проекцией вектора скорости на ось х, а второе - на ось y.
Определим эти проекции в момент времени t1=1 c.
v1x=[3*2 м/(1 с)3*(1 c)2 = 6 м/с
v1y=[4*3 м/(1 с)4*(1 с)3 = 12 м/с
В прямоугольном треугольнике, построенном на векторах [$8594$]v1, [$8594$]v1x и [$8594$]v1y
tg[$945$]=v1y/v1x=12/6=2,0
что-то до боли знакомые задачи...
Дано:
r(t) = i•A(t/[$964$])3 + j•B(t/[$964$])4 + k•С
[$964$]=1 с, А=2 м, В=3 м, С=4 м
t1 = 1 с
[$945$]=[$8736$][$8594$]v;[$8594$]x
Найти:
tg[$945$]1
Решение:
Возьмем производную от уравнения радиус вектора по времени. Получим уравнение скорости:
v(t)=r'(t)=i*(3A/т3)*t2+j*(4B/т4)*t3 (*)
В выражении (*) первое слагаемое является проекцией вектора скорости на ось х, а второе - на ось y.
Определим эти проекции в момент времени t1=1 c.
v1x=[3*2 м/(1 с)3*(1 c)2 = 6 м/с
v1y=[4*3 м/(1 с)4*(1 с)3 = 12 м/с
В прямоугольном треугольнике, построенном на векторах [$8594$]v1, [$8594$]v1x и [$8594$]v1y
tg[$945$]=v1y/v1x=12/6=2,0
Об авторе:
С уважением
shvetski
С уважением
shvetski
07.10.2020, 08:16
общий
Извините, конечно...но в ответах на эту задачу:
а) 6,0
б) 5,0
в) 4,0
г) 3,0
д) 2,0
Где, то у Вас ошибка. Посмотрите пожалуйста....
а) 6,0
б) 5,0
в) 4,0
г) 3,0
д) 2,0
Где, то у Вас ошибка. Посмотрите пожалуйста....
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