Potential energy is the energy that an object has due to its position or condition. In the case of a roller coaster, the potential energy of the coaster train is at its highest when it is at the top of the first hill. This is because the train is at its highest point above the ground, and therefore has the most potential to fall and gain kinetic energy.
Kinetic energy is the energy that an object has due to its motion. As the coaster train falls down the first hill, it gains kinetic energy. This kinetic energy is then used to carry the train through the rest of the ride, including up any subsequent hills.
The height of the first hill on a roller coaster is therefore determined by the amount of kinetic energy that the coaster train needs to have in order to complete the rest of the ride. The taller the first hill, the more potential energy the train will have, and the more kinetic energy it will be able to gain as it falls down the hill. This will allow the train to travel faster and experience more thrilling drops and turns throughout the rest of the ride.
