A car traveling at 27 m/s runs out of gas while traveling up a 9.0 ∘ slope.

Question

A car traveling at 27 m/s runs out of gas while traveling up a 9.0 ∘ slope.

How far will it coast before starting to roll back down?

Answer 1

We use the principles of conservation of energy to solve this problem. We know that the energy at the beginning is equal to the energy at the end. Since there is no potential energy at the beginning, the total energy is equal to the kinetic energy, which is equal to 1/2mv^2. At the end when the car is at rest, the total energy is equal to the potential energy, which is equal to mgh. So, we have 1/2mv^2 = mgh. We can rearrange to find that h = 1/2v^2/g. Once we find the height, we can use trigonometry and the pythagorean theorem to find the length that the car will travel.