Suppose that you and three classmates are discussing the design of a roller coaster. One says that each hill must be lower than the previous one. The second says that as long as the first hill is the highest, it doesn’t matter what height the others are. And the third says that it doesn’t matter how high any hill is relative to the others. What do you say?

I would say that I agree with the one that said that each hill must be lower than the previous one and use the principle of conservation of energy to explain.

Explanation:

Roller coaster are usually designed such that its total energy remains conserved at any point on the track. Now,  the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. At certain height on the track, the total energy of the roller coaster is in form of potential energy, which gets converted to kinetic energy as soon as it starts sliding down the hill till get to the hill's endpoint where it has maximum kinetic energy. The cycle of sliding from a high point on the track to a low point on the track means there is potential energy is converted to kinetic energy and kinetic energy then converts back to potential energy and the cycle continues.

However, due to the effect of gravity and frictional force between the track and the coaster, the energy of the coaster is gradually reduces, so it becomes a bit difficult for the coaster to move to the next hill of the same height. It is for this reason that each hill must be lower than the previous one, so that the coaster can overcome the next hill's height with its reduced energy until it loses all its energy and comes to a stop.

+15-35=-20

going in opposite directions