(III) $(a)$ Calculate the impulse experienced when a 55-kg person lands on firm ground after jumping from a height of 2.8 m. $(b)$ Estimate the average force exerted on the person's feet by the ground if the landing is stiff-legged, and again $(c)$ with bent legs. With stiff legs, assume the body moves 1.0 cm during impact, and when the legs are bent, about 50 cm. [$Hint$: The average net force on him, which is related to impulse, is the vector sum of gravity and the force exerted by the ground. See Fig. 7-34.] We will see in Chapter 9 that the force in $(b)$ exceeds the ultimate strength of bone (Table 9-2).