An astronaut stands on the surface of Vesta, which, with an average radius of 270 m, makes it the third largest object in the asteroid belt. The astronaut picks up a rock and drops it from a height of 1.5 m. He times the fall and finds that the rock strikes the ground after 3.2 s. 

(a) Determine the acceleration due to gravity at the surface of Vesta. 

(b) Find the mass of Vesta. 

(c) If the astronaut can jump to a height of 82 cm while wearing his space suit on the Earth, how high could he jump on Vesta? Assume any rotation of Vesta can be ignored.