The Moon's craters are remnants of meteorite collisions. Suppose a fairly large asteroid that has a mass of 5.00 x 10¹² kg (about a kilometer across) strikes the Moon at a speed of 15.0 km/s.

(a) At what speed does the Moon recoil after the perfectly inelastic collision (the mass of the Moon is 7.36 x 10²² kg)?

(b) How much kinetic energy is lost in the collision? Such an event may have been observed by medieval English monks who reported observing a red glow and subsequent haze about the Moon. 

(c) In October 2009, NASA crashed a rocket into the Moon, and analyzed the plume produced by the impact. (Significant amounts of water were detected.) Answer part (a) and (b) for this real-life experiment. The mass of the rocket was 2000 kg and its speed upon impact was 9000 km/h. How does the plume produced alter these results?