A ball of mass is attached to one end of a light elastic string of natural length and modulus of elasticity , where is the acceleration due to gravity. The other end of the string is fixed at a point on the line where the base of a vertical wall meets a rough horizontal plane. The ball is held on the plane a distance of from in such a way that the string lies perpendicular to the wall. Given that the coefficient of friction between the ball and the plane is , find the speed of the ball at the moment it collides with the wall. Give your answer in terms of and . If the ball rebounds from the wall with speed , at what distance from will the ball finally come to rest?