Question

A roller coaster is released from the top of a track that is 57 m high. Find the roller coaster speed when it reaches ground level.

Answer 1

Hi there!

Assuming the track is frictionless:

$E_i = E_f\\\\PE = KE\\\\mgh = \frac{1}{2}mv^2$

Cancel out the masses and rearrange to solve for velocity:

$gh = \frac{1}{2}v^{2}\\\\v = \sqrt{2gh}$

Plug in the given height and let g = 9.8 m/s²:

$v = \sqrt{2(9.8)(57)} = \boxed{33.42 m/s}$