For a uniform gravitational field:

$\begin{array}{rcl}\mathbf{U}\mathbf{\left(}{\mathbf{y}}_{\mathbf{f}}\mathbf{\right)}\mathbf{-}\mathbf{U}\mathbf{\left(}{\mathbf{y}}_{\mathbf{0}}\mathbf{\right)}& \mathbf{=}& \mathbf{-}{\mathbf{\int}}_{{\mathbf{y}}_{\mathbf{0}}}^{{\mathbf{y}}_{\mathbf{f}}}{\mathbf{F}}_{\mathbf{g}}\mathbf{\xb7}\mathbf{d}\mathbf{s}\end{array}$

But gravitational potential energy, U = mgh

Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find

Where

Express your answer in terms of m, g, y_{0}, and y_{f}.

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