1.  

A ball (with m) is thrown with velocity v (the angle wr.t. horizontal direction is a). The ball then hits the wall and rebounds. If the horizontal distance between the initial position of the ball and the wall is L, find an appropriate angle to have the ball return to its initial position. Assume the coefficient of restitution is 0.5. No need to specify the final answer, just derive the final equation for solving the angle.