Question

If I am driving a 1000 kg car at a speed of 15 m/s at the bottom of a hill and let the car coast (NO
more gas given to the car) how high up the hill will the car be able to reach? SHOW YOUR WORK

Answer 1

If we assume zero friction, then all kinetic energy of car at the bottom of the hill converts to the potential energy of its at the top of the hill:

$$\dfrac{mv^2}{2}=mgh$$

where $m = 1000kg$ is the mass of the car, $g = 9.81m/s^2$ is the gravitational acceleration, $h$ is the height of the hill, and $v = 15m/s$ is the speed of the car at the bottom of the hill. Thus, obtain:

$$h = \dfrac{v^2}{g}\\ h=\dfrac{15^2}{9.81} \approx 22.9m$$

Answer. 22.9 m.