A cart of mass m1 = 10 kg slides down a frictionless ramp and is made to collide with a second cart (initially at rest) of mass m2 = 20 kg, which then heads into a vertical loop of radius 0.25 m as shown in Figure P7.66. Derive the expression of height h, in terms of radius r, from which cart 1 would need to start to make sure that cart 2 completes the loop without leaving the track and, hence, determine the value of h. Assume an elastic collision.