Answer to Question #143683 in Physics for Sydney

Question

Wendy is resting on her bike at the top of a 225 meter tall hill. She releases the brake and begins to roll down the hill. If Wendy and the bike has a total mass of 75.0 kg, what is the speed of the bike when it reaches the bottom of the hill and begins coasting?

Answer 1

If we assume zero friction, then all potential energy of Wendy and the bike at the top of the hill converts to the kinetic energy of their movement at the bottom of the hill:

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

where $m = 75kg$ is the mass of the Wendy and bike, $g = 9.81m/s^2$ is the gravitational acceleration, $h = 225m$ is the height of the hill, and $v$ is the speed of the bike at the bottom of the hill. Thus, obtain:

$$v = \sqrt{2mgh}\\ v = \sqrt{2\cdot 9.81\cdot 225} \approx 66.44m/s$$

Answer. 66.44 m/s.