Question

A roller coaster has a mass of 250 kg. It drops from rest at the top of a hill that's 88 m tall. How fast is it going when it reaches the bottom?

Answer 1

The velocity at the bottom of the hill will be approximately `41.5` m/s.

Explanation:

Here, assuming no energy is dissipated by friction or air resistance, all the gravitational potential energy it has at the top of the hill is converted to kinetic energy at the bottom of the hill. Therefore, we have:

`mgh = 1/2mv_"final"^2`

We want to solve for `v`, therefore

`2gh = v_"final"^2`

`sqrt(2gh) = v_"final"`

`sqrt(2(9.8)(88)) = v_"final"`

`41.5 m/s = v_"final"`

Hopefully this helps!