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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.

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MathPhys

Answer:

v = √(2 MGh) / R

Explanation:

Assuming that h is much smaller than R, we can say the acceleration of gravity is approximately constant during the fall.

Potential energy = Kinetic energy

mgh = 1/2 mv²

v = √(2gh)

v = √(2 (MG/R²) h)

v = √(2 MGh) / R

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