On a frictionless horizontal surface, assumed to be the x-y plane, a small trolley A is moving along a straight line parallel to the y-axis (see figure) with a constant velocity of
(a) The motion of the ball is observed from the frame of the trolley. Calculate the angle θ made by the velocity vector of the ball with the x-axis in this frame.
(b) Find the speed of the ball with respect to the surface, if φ = 4θ /3 .
Solution: (a) If the trolley A is at rest, anything that comes to hit it must be along the line OA, so the angle should bewith the x- axis.
(b) Let the ball is given a velocity v at an angle φ = 4θ /3, where, the angle we get is . The observer at trolley will see it coming at angle so the relative velocity . will have same x and y components.
Now the x- component of=
and the y -component of