# 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.)

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Conservative Forces & Inclined Planes concept. You can view video lessons to learn Conservative Forces & Inclined Planes. Or if you need more Conservative Forces & Inclined Planes practice, you can also practice Conservative Forces & Inclined Planes practice problems.