The spring bumper is used to arrest the motion of the 4-lb block, which is sliding toward...

The spring bumper is used to arrest the motion of the 4-lb block, which is sliding toward it at v = 9 ft/s. As shown, the spring is confined by the plate P and wall using cables so that its length is 1.5 ft. If the stiffness of the spring is k = 50 lb/ft, determine the required unstretched length of the spring so that the plate is not displaced more than 0.2 ft after the block collides into it. Neglect friction, the mass of the plate and spring, and the energy loss between the plate and block during the collision.