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.

Mass of the object m = m
Mass of the planet M = M
Radius of the planet R = R
Height h = h
Total energy at height h is E = Potential energy at height h
                                          = -GMm/(R+h)
Total energy at the surface of the planet E ' = [-GMm/R] + ( 1/ 2) mv ²
From law of conservation of energy , E = E '

-GMm/(R+h) =  [-GMm/R] + ( 1/ 2) mv ²
( 1/ 2) mv ² = [-GMm/(R+h) ] +[GMm/R]

             v ² = [-2GM/(R+h) ] +[2GM/R]

                  = [-2GMR +2GM(R+h)]/[(R+h)R]

                 = 2GMh / [(R+h) R ]

             v = √ {2GMh / [(R+h) R ]}