Gravity and Energy -- Two masses above two different planets

[jstelpend]

Homework Statement

Hello, I have been stuck on this problem.

A ball with an unknown mass (mA) is initially 11.9 meters above the surface of a foreign planet. A box with an unknown mass (mE) is initially some distance (hE) above the surface of the Earth. The ball and box both have the same GPE relative to the surface of their respective planets.

The foreign planet has a mass of 8.7 x 10^24 kg and its radius is 6.35 x 10^6 meters.

Both the ball and the box are dropped from rest and caught by someone on the surface of the respective planets. The person on the foreign planet and the person on the Earth both apply the same amount of impulse on their respective objects.

Find hE initially. (6.67*10^-11 to be used for G and 9.8 to be used for g of Earth. Also, ignore air resistance)

Relevant Equations

Conservation of energy, gravitational acceleration, Fg = GMm/d^2???, pi = pf

So far, I have found g of the foreign planet, Vf of the ball, and realize that GPEiA = KEfA (Am I right here?). Thus, since GPEiA = GPEiE, GPEiE also equals KEfE. I also understand that, since the same impulse is applied to catch the objects, both objects have the same momentum at the moment that they are caught.

I am stuck on finding the mass of the ball which, I believe, will allow for me to solve the entirety of the question.

I appreciate all help and thank, in advance, those who decide to reach out!

 

[haruspex]

I am stuck on finding the mass of the ball

Seems to me that you don't need to know the two masses, only their ratio.