What is the terminal velocity that a 40-hp car will attain when it coasts down a 10% grade? What is the max velocity it reaches on a flat road? Assume that the car weighs 3,200 lb, has a frontal area of 30 sq feet, and a drag coefficient of 0.55.

Question

mrnood · Answer

First thing to clear up is the units in the question.

"Pounds" is a unit of MASS not Weight.

I assume this error has been used throughout your study, so please clarify what it really means -
1 pound mass acting under gravity exerts a force of 1 lbf (pound force)
1 pound mass having acceleration if 1 ft/s^2 requires a force of 1 poundal (pdl)

Does the question mean
 
the MASS of the car is 3,200 lbs, 
or that it's weight is 3200lbf
or that its weight is 3200 pdls

Once that is clear you can calculate the force acting along the gradient (you know Tantheta = 0.1 for 10% grade)

The termainal velocity will be when the resistive force due to air resistance = force along the gradient.
The resistive force is given by 1/2 * rho * CD * A * V^2
(you have all that except rho (density of air -  look it up))

On the flat the power to overcome the drag force is FxV

The top speed will be when the power of the engine (40 HP) = drag power