(6%) Problem 7: The Moon\'s craters are remnants of meteorite collisions. Suppos

Question

(6%) Problem 7: The Moon's craters are remnants of meteorite collisions. Suppose a fairly large asteroid that has a mass of 5.1 x 1012 kg (such an asteroid is about a kilometer across) strikes the Moon at a speed of 17.5 km/s relative to the Moon. 50% Part (a) At what speed in meters per second, does the Moon recoil after the perfectly inelastic collision? The mass of the Moon is 7.36 x 102 kg? 50% Part (b) what is the change in kinetic energy, in ules 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. Grade Summary Deductions Potential 0% 100%

Explanation / Answer

Here ,

let the recoild speed is v

Using conservation of momenetum

5.1 *10^12 * 17500 = (5.1*10^12 + 7.36 *10^22) * v

v = 1.2 *10^-6 m/s

the recoil speed of moon is 1.2 *10^-6 m/s

b)

kinetic energy lost = iniital kinetic energy - final kinetic energy

kinetic energy lost = 0.5 * 5.1 *10^12 * 17500^2 - 0.5 * (5.1 *10^12 + 7.36 *10^22) * (1.2*10^-6)^2

kinetic energy lost = 7.8*10^20 J

the kinetic energy lost is 7.8 *10^20 J

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