Question

You have been asked to make a roller coaster more exciting. The owners want the speed at the bottom of the first hill tripled. How much higher must the first hill be built?

Answer 1

Relationship between speed at bottom of hill, speed at top of hill, acceleration, and height of hill is given by\[v ^{2}=u ^{2}+2as\]
(u = 0, a = g in this case, before and after height increase)

Find required multiple of original height.
For v to increase threefold, v squared (SUPERSCRIPT 2) must increase ninefold...
...therefore s must increase ninefold.

Answer 2

Consider the problem in terms of potential and kinetic energy and assume that at the top of the hill the train's energy is entirely potential energy, while at the bottom the trains energy is entirely kinetic energy. The solution should be quickly apparent.