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/s².

1. 10 m/s
2. 20 m/s
3. 100 m/s
4. 40 m/s
5. 0 m/s

Answer 1

10 m/s

Step-by-step explanation:

mass, M = 2000 kg

Power, P = 100 kW = 100000 W

inclination, θ = 30°

g = 10 m/s^2

Let the velocity is v.

P = F x v

where, F is force and v be the velocity

100000 = mg Sin 30 x v

100000 = 2000 x 10 x 0.5 x v

v = 10 m/s

Thus, the speed is 10 m/s.