Question

A small asteroid that has a mass of 100 kg is moving at 200 m/s when it is 1110 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.)

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.) IN MEGAJOULES (MJ)

Specifically need help with number 2!

Answer 1

1] By conservation of energy

Initial Potential energy + Initial Kinetic energy = Final potential energy + final kinetic energy

-GMm/(R+h) + 0.5mu^2 = -GMm/(R) + 0.5mv^2

-6.67e-11*7.458e22*100/(1737000+1110000) + 0.5*100*200^2 = -6.67e-11*7.458e22*100/1737000+ 0.5*100*v^2

v = 1508 m/s answer

2] Work done = change in KE = - 0.5*mv^2 = -0.5*100*1508^2 = -113703200 J = - 113.7 MJ Answer