Q: On a frictionless horizontal surface, assumed to be the XY-plane, a small trolley A is moving along a straight line parallel to the Y-axis (as shown in figure) with a constant velocity of ( √3-1) m/s . At a particular instant, when the line OA makes an angle of 45° with the X-axis, ball is thrown along the surface from the origin O. Its velocity makes an angle φ with the X-axis and it hits the trolley.

(a) The motion of the ball is observed from the frame of the trolley. Calculate the angle q made by the velocity vector of the ball with the X0axis in this frame.

(b) Find the speed of the ball with respect of the surface, it φ = 4θ/3.