# Problem: A car is parked at the top of a 52m -high hill. It slips out of gear and rolls down the hill.How fast will it be going at the bottom? (Ignore friction.)

###### FREE Expert Solution

Law of conservation of energy:

$\overline{){\mathbf{P}}{{\mathbf{E}}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbf{K}}{\mathbf{.}}{{\mathbf{E}}}_{{\mathbf{0}}}{\mathbf{=}}{\mathbf{P}}{{\mathbf{E}}}_{{\mathbf{f}}}{\mathbf{+}}{\mathbf{K}}{\mathbf{.}}{{\mathbf{E}}}_{{\mathbf{f}}}}$

$\begin{array}{rcl}\begin{array}{rc}\mathbf{m}\mathbf{g}{\mathbf{h}}_{\mathbf{0}}& \mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}\end{array}& \mathbf{=}& \begin{array}{rc}\mathbf{m}\mathbf{g}{\mathbf{h}}_{\mathbf{f}}& \mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\end{array}\end{array}$

###### Problem Details

A car is parked at the top of a 52m -high hill. It slips out of gear and rolls down the hill.

How fast will it be going at the bottom? (Ignore friction.)