Designing a Roller Coaster: Higher Hills After the First? Explained.

[jack1234]

Question
In the design of a roller coaster, is it possible for any hill of the ride to
be higher than the first one? If it is not possible, give the reason. If it is
possible, how is it done?

Attempts
It is possible. Says we make the second hills higher than the first one, we can achieve this by providing more kinetic energy when the roller coaster cross the first hill, and hence the kinetic energy plus the potential energy of the first hill, will make the roller coaster pass through the higher second hill with less kinetic energy.

Is it correct? If no, what is the better answer?

 

[Ryo124]

If you have nothing that "speeds up" the coaster car at the bottom of the first hill, than no it is not possible.
If you do have something that speeds up the car at the bottom of the first hill, than it is possible.

At the top of the first hill, assuming the coaster is not moving, all energy is potential and kinetic energy is zero.

At the bottom of the hill, all the energy is transferred to kinetic energy and potential energy is zero.

In an ideal situation, the second hill cannot be higher because it would have to take more energy than what was originally there when the coaster car was atop the first hill.

Read about conservation of energy for a better understanding. If this answer is incomplete, than someone please "complete" it.