The engine of a 2000 kg mercedes going up pike’s peak delivers energy to its drive wheel at the rate 100 kw . neglecting air resistance, what is the largest speed the car can sustain on the steep pike’s peak mountain highway, where the road is 30◦ to the horizontal? the acceleration due to gravity is 10 m/s 2 . 1. 40 m/s 2. 10 m/s 3. 20 m/s 4. 0 m/s 5. 100 m/s

2. 10 m/s

Explanation:

There are two forces acting on the car along the inclined plane:

- The driving force of the car, F, pulling upward along the ramp

- The component of the weight of the car, , pulling downward along the ramp

In order to go at constant speed, the acceleration must be zero, so the net force must be zero. Therefore we can write:

From which we can find the driving force of the car:

The power of the engine is the product between force and speed of the car:

since we know the power, , we can find the speed: