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 .

Answer 1

Answer:

v = 10 m/s

Explanation:

given,

Mass of Mercedes engine = 2000 Kg

Power delivered = 100 kW

angle made with horizontal = 30°

acceleration due to gravity =  10 m/s²

largest speed car can sustain = ?

we know,

Power = Force x velocity

P = F x v

P = mg sinθ x v

P = mg sin 30° x v

P = 0.5 mg  x v

$v = \dfrac{100 \times 10^3}{0.5\times 2000 \times 10}$

v = 10 m/s

hence, the maximum velocity is equal to v = 10 m/s