A car goes up an incline that makes an angle of 20 degrees with the horizontal. If the car has a mass of 1600 kg, and the engine is capable of generating 32000 W of usable power, what is the maximum velocity the car can go at? Take the acceleration of gravity to be 9.81 ms2.

V = 5.96 m/s

Explanation:

First we find the force required to move the car up the inclined plane. This force shall be equal to the component of the weight of the car that is parallel to the inclined plane. Hence,

F = W Sin θ

F = mg Sin θ

where,

F = Force = ?

m = mass of car = 1600 kg

g = 9.8 m/s²

θ = Inclination Angle = 20°

Therefore,

F = (1600 kg)(9.8 m/s²) Sin 20°

F = 5362.87 N

Now, we use power formula:

P = FV

V = P/F

where,

P = Engine Power = 32000 W

V = Maximum Velocity of Car = ?

Therefore,

V = 32000 W/5362.87 N

V = 5.96 m/s

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