A rock climber of weight W has a rope attached a distance h below him for protection. Supp...

A rock climber of weight W has a rope attached a distance h below him for protection. Suppose that he falls, and assume that the rope behaves like a linear spring with unstretched length h and spring constant k = C/h, where C is a constant. Use conservation of energy to determine the maximum force exerted on the climber by the rope. (Notice that the maximum force is independent of h, which is a reassuring result for climbers: The maximum force resulting from a long fall is the same as that resulting from a short one.)