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

Step-by-step 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=(1)/(2) m v^(2)+O \\&m g h=(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=(l)/(2) v^(2) \\&h=(1)/(2) * (v^(2))/(g) \\&h=(1)/(2) * (3.5^(2))/(9.8) \\&h=0.625 \mathrm{~m}\end{aligned}`

Therefore, the required height of hill is 0.625 m