Question

A roller coaster that descended 20 m in height and had an initial speed of 5 m/s downhill. Suppose the roller coaster had had an initial speed at the bottom of the hill of 5 m/s uphill instead, and it coasted 20 m uphill, stopped, and then rolled back down to a final point at the same elevation as it started. We would find in that case that its final speed is the same as its initial speed. Explain in terms of conservation of energy.

a) Conservation of energy does not apply in this scenario.
b) Initial and final speeds are different.
c) Conservation of energy implies equal initial and final speeds.
d) Conservation of energy implies opposite initial and final speeds.

Answer 1

The final speed of the roller coaster is the same as its initial speed due to the conservation of energy.

Step-by-step explanation:

The final speed of the roller coaster when it reaches the same elevation as its starting point is the same as its initial speed.

This can be explained in terms of conservation of energy. When the roller coaster is at the highest point of the hill, it has gravitational potential energy.

As it goes downhill, this potential energy is converted to kinetic energy, which is responsible for the speed of the roller coaster.

When the roller coaster reaches the same elevation as its starting point, it has regained its initial potential energy, which is then converted back to kinetic energy.

Since the roller coaster started with the same initial speed, the final speed is also the same.