*Answer:*
When the car is traveling on a level road at its maximum speed, , then all
of the power output, , of its engine is used to overcome the power
dissipated by the resistive force, . Hence,

where the left-hand side is the power output of the engine, and the right-hand side is the power dissipated by the resistive force (

When the car, whose weight is , is traveling up an incline, whose angle with respect
to the horizontal is , it is subject to the additional
force
, which acts to impede its motion.
Of course, this force is
just the component of the car's weight acting down the incline. Thus, the
new power balance equation is written

where is the maximum velocity of the car up the incline. Here, the left-hand side represents the power output of the car, whereas the right-hand side represents the sum of the power dissipated by the resistive force and the power expended to overcome the component of the car's weight acting down the incline. It follows that