Help With This Physics Question?

Question

Two objects A and B are connected by a

rigid rod that has a length 32 m. The objects

slide along perpendicular guide rails.

If A slides to the left with a constant speed

70.1424m/s along the x-axis, find the velocity

of B along the y-axis when the rod makes an

angle 28◦ with the x-axis. Answer in units of

m/s.

Thanks in advance :)

Answer 1

This is a related rates question.

I am assuming that initially the rod is positioned vertically on the positive y axis.

When the angle is 28°,

x = 32cos 28° = 28.25

y = 32sin 28° = 15.02

The general equation is

x^2 + y^2 = 32^2

Differentiating with respect to time,

2x(dx/dt) + 2y(dy/dt) = 0

dy/dt = -x(dx/dt)/y = - (28.25)(70.1424)/(15.02) = - 131.9 m/s