**70. A 1900-kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 27 m/s. Going up a hill, the car’s engine produces 47 hp more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?

F_R is the combine force of air resistance and friction, F_EU is the force provided by the engine when the car is going uphill, and F_ED is the force provided by the engine when the car is going downhill. Since the velocity is constant when the car is going up and down yield the following sum of force equations parallel to the incline.

Going uphill

At constant speed we can write power as

Using forces found above

Now solve for sin(q)

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This page last updated on January 11, 2020