Question

A roller coaster car rolls down a frictionless track, reaching a speed v at the bottom. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? Does you answer to part a depend on whether the track is straight or not? Explain

Answer 1

By a factor of
`√(2)`

Step-by-step explanation:

The relationship between potential energy and the velocity of an object can be expressed with the following formula: m.g.h =
`(1)/(2)m v^(2)`

According to the example in the question, for the velocity of the rollercoaster to be twice as much as it was before, the height of the track must be increased by a factor of
`√(2)` of it's original height.

Of course if the track is not straight and if it has a curve, the factor to multiply its height is going to be different since the acceleration of the rollercoaster is going to be different.

I hope this answer helps.