Question

A roller coaster ride in a park includes a vertical drop of 60m. Assume that the roller coaster has a speed of nearly zero when it reaches the top of the hill. Neglected friction, find the speed of the riders at the bottom of the hill. Show complete solution.

Answer 1

The law of conservation of energy says

$$E_i=E_f$$

Total mechanical energy is a sum of kinetic and potential energy. So

$$E_i=\frac{mv^2}{2}+0$$

$$E_f=0+mgh$$

Therefore

$$\frac{mv^2}{2}=mgh$$

Finally

$$v=\sqrt{2gh}=\sqrt{2*9.8*60}=34.5\:\rm m/s$$