Question

You can, in an emergency, start a manual transmission car by putting it in neutral, letting the car roll down a hill to pick up speed, then putting it in gear and quickly letting out the clutch. If the car needs to be moving at 3.5 m/s for this to work, how high a hill do you need? (You can ignore friction and drag)

Answer 1

Answer:

The hill should be not less than 0.625 m high

Explanation:

This problem can be solved by using the principle of conservation of mechanical energy. In the absence of friction, the total mechanical energy is conserved. That means that

$E_m=U+K$ is constant, being U the potential energy and K the kinetic energy

$U=mgh$

$K=\frac{mv^2}{2}$

When the car is in the top of the hill, its speed is 0, but its height h should be enough to produce the needed speed v down the hill.

The Kinetic energy is then, zero. When the car gets enough speed we assume it is achieved at ground level, so the potential energy runs out to zero but the Kinetic is at max. So the initial potential energy is transformed into kinetic energy.

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

We can solve for h:

$h=\frac{v^2}{2g}=\frac{3.5^2}{2(9.8)}=0.625m$

The hill should be not less than 0.625 m high