# Problem: 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 = _____

###### FREE Expert Solution

Potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{G}{\mathbf{M}}_{\mathbf{1}}{\mathbf{M}}_{\mathbf{2}}}{\mathbf{R}}}$

Kinetic Energy:

$\overline{){\mathbf{K}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

Potential at height h — initial potential energy:

${{\mathbf{U}}}_{{\mathbf{R}}{\mathbf{+}}{\mathbf{h}}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{GMm}}{\mathbf{R}\mathbf{+}\mathbf{h}}$

Initial kinetic energy:

$\mathbit{K}{\mathbit{E}}_{\mathbf{0}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbit{m}{{\mathbit{v}}_{\mathbf{0}}}^{\mathbf{2}}$

Potential at the surface of the planet — final potential energy:

${{\mathbf{U}}}_{{\mathbf{R}}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{GMm}}{\mathbf{R}}$

Final kinetic energy: ###### Problem Details

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 = _____