A car of mass 1100 kg starts from rest at sea level and climbs a hill of altitude 50 m. At the

top of the hill the car has a speed of 25 m/s. From the top of the hill the driver turns off the
engine and coasts down to an altitude of 15 m. Assume the friction and the air resistance to be
negligibly small.
A. What is the speed of the car when the altitude is 15m?
B. ) After passing the altitude of 15m, the driver climbs up again, without turning the engine on. In
this case, the speed of the car would be zero at an altitude of _____?

To solve this problem, we need to use the principles of conservation of mechanical energy. The total mechanical energy of the car is the sum of its potential energy and kinetic energy.

A. To find the speed of the car when the altitude is 15 m, we can equate the initial mechanical energy of the car at the top of the hill to its mechanical energy at the altitude of 15 m.

1. Calculate the initial potential energy at the top of the hill:
Potential energy = Mass * Gravitational acceleration * Height
Potential energy = 1100 kg * 9.8 m/s^2 * 50 m

2. Calculate the final mechanical energy at the altitude of 15 m:
Final mechanical energy = Potential energy + Kinetic energy
Since the car is coasting and there is no engine or external force acting on it, the kinetic energy remains constant.
Final mechanical energy = Potential energy + Initial kinetic energy

3. Equate the initial mechanical energy to the final mechanical energy:
1100 kg * 9.8 m/s^2 * 50 m = 1100 kg * 9.8 m/s^2 * 15 m + (1/2) * 1100 kg * v^2

Solving this equation will give you the speed (v) of the car when the altitude is 15 m.

B. To find the altitude where the car's speed would be zero, we need to consider the conservation of mechanical energy again. At the top of the second hill, the car will have the same initial mechanical energy as it did at the top of the first hill.

1. Calculate the initial potential energy at the top of the hill:
Potential energy = Mass * Gravitational acceleration * Height
Potential energy = 1100 kg * 9.8 m/s^2 * 50 m

2. Set the final mechanical energy (when the speed is zero) equal to the initial mechanical energy and calculate the height.
1100 kg * 9.8 m/s^2 * 50 m = 1100 kg * 9.8 m/s^2 * h

Solving this equation will give you the altitude (h) at which the car's speed would be zero.