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:

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.