Question

A 1860 kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down hill at 38.9 m/s. Going up hill, the car's engine needs to produce 66.4 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?

Answer 1

Let the subscripts u and d indicate physical quantitities for the motion up the hill and down the hill respectively.

The power and force that is exerted by the car engine are related as

The velocity vector is along the direction of force for both uphill and down hill motion. So, the angle between the vectors is zero degrees. Thus,

The free body diagram of the car in shown below for the uphill and down hill motion.

Since in both cases the car moves with constant velocity we get Newton's second law of motion,

where F_f is the force due to friction, which is same in both cases. So, if we subtract eq. 2 from eq. 1, we get