The Moon\'s craters are are remnants of meteorite collisions. Suppose a fairly l

Question

The Moon's craters are are remnants of meteorite collisions. Suppose a fairly large asteroid has a mass of 4.95 x10^12 kg (such as an astroid is about a kilometer across) strikes the Moon at a speed of 15.5 km/s relative to the Moon. A.) At what speed in, meters per second, does the Moon recoil after the perfectly inelastic collison? The mass of the Moon is 7.36 x 1022 kg? B.) What is the change in kinetic energy, in joules, in the collison? Such an event may have been observed by midevil English monks who reported observing a red glow and subsequent haze about the moon.

Explanation / Answer

a) From connservstion of momentum

ma ua + mm um = (ma + mm) * v

v = (4.95 * 1012 * 15.5 * 103) / (4.95 * 1012 + 7.36 * 1022)

= 1.04 * 10-6 m/s

b) change in KE = 1/2 ma ua2 - 1/2 (ma + mm) * v2

= (0.5 * 4.95 * 1012 * (15.5 * 103)2) - (0.5 * (4.95 * 1012 + 7.36 * 1022) * (1.04 * 10-6)2)

= 5.95 * 1020 J

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