Question

Two objects, A and B, are connected by hinges to a rigid rod that has a length L. The objects slide along perpendicular guide rails as shown in the figure below. Assume object A slides to the left with a constant speed v.
(a) Find the velocity vB of object B as a function of the angle θ. (Use any variable or symbol stated above as necessary.)
vB =

(b) Describe vB relative to v. Is vB always smaller than v, larger than v, or the same as v, or does it have some other relationship?

Answer 1

According to the questions statements it shows

y= L sin (theta)

and as it shows A and B are right triangle

y= sqrt (L^2 - x^2)

we need to find the speed of B by differentiating w.r.t time.
so,

d/dt = dx/dt . d/dx = -v d/dx

-v represents the A's velocity
so,
Vb = d/dt (y) = -v d/dx sqrt(L^2-x^2)
= v.x/ sqrt(L^2-x^2)

x/ sqrt(L^2-x^2) = cot (theta)

hence

Vb = vcot (theta)