The free-fall acceleration on a large asteroid, in the vacuum of space, is 0.15 m/s^2. A spacecraft hovering 500 m above the surface drops a 25 kg payload wrapped in a padded jacket. What is the payload's impact speed?

(I) By how much does the gravitational potential energy of a 58-kg pole vaulter change if her center of mass rises 4.0 m during the jump?

(II) A sphere of radius r₁ has a concentric spherical cavity of radius r₂ (Fig. 8–42). Assume this spherical shell of thickness r₁ - r₂ is uniform and has a total mass M. Show that the gravitational potential energy of a mass m at a distance r from the center of the shell ( r > r₁ ) is given by

U = - (GmM/r).

<IMAGE>