A small asteroid that has a mass of 100 kg is moving at 200 m/s when it is 1220

Question

A small asteroid that has a mass of 100 kg is moving at 200 m/s when it is 1220 km above the Moon. 1) How fast will the meteorite be traveling when it impacts the lunar surface if it is heading straight toward the center of the Moon? (Express your answer to three significant figures.) mSubmit You currently have O submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question 2) How much work does the Moon do in stopping the asteroid if neither the Moon nor the asteroid heats up in the process? (Express your answer to three significant figures.) MJ Submit You currently have O submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question.

Explanation / Answer

1) Applying energy conservation,

PEi + KEi = PEf + KEf

- G M m / r0 + m v0^2 /2 = - G M m / R + m v^2 /2

v^2 = - 2 G M /r0 + 2 G M / R + v0^2

v0 = 200 m/s

r0 = (1737 + 1200 ) 10^3 = 2957 x 10^3 m

R = 1737 x 10^3 m

G = 6.67x 10^-11

M = 7.348 x 10^22 kg

v = 1545 m/s

(2) Work done = 100 (1545^2 - 0) /2

= 119.4 x 10^6 J

= 119.4 MJ

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