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

Question

The Moon's craters are remnants of meteorite collisions. Suppose a fairly large asteroid that has a mass of 5.00 times 10^12 kg (about a kilometer across) strikes the Moon at a speed of 15.0 km/s. At what speed does the Moon recoil after the perfectly inelastic collision (the mass of the Moon is 7.36 times 10^22 kg)? 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, 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 after these results?

Explanation / Answer

Here ,

let the recoild speed is v

Using conservation of momenetum

5 *10^12 * 15000 = (5 *10^12 + 7.36 *10^22) * v

v = 1.02 *10^-6 m/s

the recoil speed of moon is 1.02 *10^-6 m/s

b)

kinetic energy lost = iniital kinetic energy - final kinetic energy

kinetic energy lost = 0.5 * 5 *10^12 * 15000^2 - 0.5 * (5 *10^12 + 7.36 *10^22) * (1.02*10^-6)^2

kinetic energy lost = 5.625 *10^20 J

the kinetic energy lost is 5.625 *10^20 J

c)

for the recoil speed ,

Using consevration of momentum

2000 * (9000 * 5/18) = (2000 + 7.36 *10^22) * v

solving for v

v = 6.79 *10^-17 m/s

the recoil speed is 6.79 *10^-17 m/s

d)

kinetic energy lost = initial kinetic energy - final kinetic energy

kinetic energy lost = 0.5 * 2000 * (9000 * 5/18)^2 - 0.5 * (2000 + 7.36 *10^22) * (6.79 *10^-17)^2

kinetic energy lost = 6.25 *10^9 J

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