A small asteroid that has a mass of 100 kg is moving at 200 m/s when it is 1000 km above the surface of the Moon.

Question

A small asteroid that has a mass of 100 kg is moving at 200 m/s when it is 1000 km above the surface of the Moon.

a. How fast will the meteorite be traveling when it impacts the lunar surface if it is heading straight toward the center of the Moon?

b. The atmosphere of the Moon is negligible. How much work does the Moon do in stopping the asteroid? The radius and mass of the Moon are 1.737 × 10^6 m and 7.35 x 1022 kg, respectively.

Note: Can someone help me solve these problems using techniques learned in an AP Algebra-based Physics class?

Answer 1

Hi Diane!

Hopefully you've already seen that this problem is one of non-constant acceleration, and since you're in an algebra-based course, this means you can't use kinematics for (a). Let's try using energy instead!

Is energy conserved in this problem? Yes, since there are no none-conservative forces at play. Therefore, if we consider state A to be at 1000km and B to be at the surface:

E_A = U_{G, A} + KE_A = U_{G, B} + KE_B

When solving this equation, we want to use U_G = -GM_moonm_meteor/r, not mgh - because acceleration due to gravity will vary over this large scale! And crucially, for state A, r = radius of moon + 1000 km, since r is measured from the center of the moon.

Once you have solved for part (a), note that the moon brings the meteor to rest, so it does negative work equal to the object's kinetic energy upon impact (by the work-kinetic energy theorem).

Hope this helps!