Physics Question

Question

A roller coaster goes over a 15 m tall hill then approaches a 29 m hill. What is the minimum velocity the roller-coaster would need when going over the 15 m hill to make it to the top of the 29 m hill?

Answer 1

This is a conservation of mechanical energy question

Suppose the minimum velocity is v

Then mechanical energy at top of 15m hill is 0.5 m v² + mgh = 0.5 mv² + 15mg

g = 9.81 m/s/s (acceleration due to gravity).

All of this (assuming no loss due to friction) is converted to potential energy at top of 29m hill

So 0.5 m v² + 15mg = 29mg

You can solve this for v