Question

7-The 2000 kg car is moving at 10 m/s and has just run out of gas. The driver quickly shifts into neutral and hopes that he or she can roll to the gas station which is just over the next hill. Assuming negligible friction, under what condition will he make it? Back up your answer with a calculation and a brief explanation.

Answer 1

When the driver shifts the car into neutral, all the energy is present in the form of kinetic energy.

Since friction is negligible, there won't be energy losses due to friction.

Gas station is over the next hill. When the car goes up the hill, its kinetic energy will be converted into potential energy.

So, the car will continue to climb the hill till its entire kinetic energy is converted into potential energy

∴ initial kinetic energy = final potential energy

Here, m = mass of car

v = initial velocity of car

g = acceleration due to gravity

h = height travelled by car

So, the maximum height that the car can reach is 5.097m

So,the driver can reach the gas station is the height of hill is less than or equal to 5.097m