Derive the expression for the range of the ball as a function of its height. To do this you should use the following steps. In the first part of the motion, the ball undergoes vertical free fall until it hits the bounce plate. At this point, its final velocity in the y-direction becomes the initial velocity in the x-direction after hitting the plate. a. Calculate the time it takes the ball to hit the ground after hitting the bounce plate. b. Find the distance that the ball will travel in the horizontal direction in this time.