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

Answer 1

Answer: 0.625 m

Explanation:

Given:

Final velocity of the car = 3.5 m/s

While the car rolls down the hill, there is a conversion of potential energy (PE)  to kinetic energy (KE). Therefore, applying the conversion of energy as,

$Total energy at height (\mathrm{h})= Total energy at bottom \begin{aligned}&K E+P E=K E^{\prime}+P E^{\prime} \\&0+m g h=\frac{1}{2} m v^{2}+O \\&m g h=\frac{1}{2} m v^{2}\end{aligned}$

Here, m denotes the mass of the car, g is the gravitational acceleration, having a value of 9.8 m/s^2.  And h is the height of the hill.

Solving for h,

$\begin{aligned}&g h=\frac{l}{2} v^{2} \\&h=\frac{1}{2} \times \frac{v^{2}}{g} \\&h=\frac{1}{2} \times \frac{3.5^{2}}{9.8} \\&h=0.625 \mathrm{~m}\end{aligned}$

Therefore, the required height of hill is 0.625 m