An object of mass m is dropped from height h above a planet of mass m and radius r .

find an expression for the object's speed as it hits the ground.
express your answer in terms of the variables m, m,h, r and appropriate constants.

v=

Explanation:

The initial mechanical energy of the object, when it is suspended at a height h above the planet of radius R and mass M, is just gravitational potential energy, so

When the object reaches the ground, its mechanical energy is now sum of its kinetic energy Kf and its new gravitational potential energy Uf:

Since the mechanical energy is conserved, we can write

Ei = Ef

So we can write

from which we can find an expression for v, the speed of the object when it hits the ground:

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