Question

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

Answer 1

Option (2) is correct.

Speed of car in upward direction = v x sin(theta)

Power of the wheel = m x g x v x sin (theta)

m= mass of the car

g = acceleration due to gravity

v = velocity of the car

v = Power/( m x g x sin(30))

= 100 x 1000 W / ( 2000 Kg x 10 m/s^2 x 0.5)

= 10m/s

= 36km/h

Answer 2

2. 10 m/s

Step-by-step 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,
`mg sin \theta`, 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:

`F-mgsin \theta =0`

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

`F=mgsin \theta=(2000 kg)(10 m/s^2)(sin 30^(\circ))=10,000 N`

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

`P=Fv`

since we know the power,
`P=100 kW=100,000 W`, we can find the speed:

`v=(P)/(F)=(100,000 W)/(10,000 N)=10 m/s`