The maximum torque output from the engine of a new experimental car of mass m is \tau. The maximum rotational speed of the engine is \omega. The engine is designed to provide a constant power output P. The engine is connected to the wheels via a perfect transmission that can smoothly trade torque for speed with no power loss. The wheels have a radius R, and the coefficient of static friction between the wheels and the road is \mu. What is the maximum sustained speed v the car can drive up a 30 degree incline? Assume no frictional losses and assume \mu is large enough so that the tires do not slip.
Answer Choices
A. v=2 P /(m g)
B. v=2 P /(\sqrt{3} m g)
C. v=2 P /(\mu m g)
D. v=\tau \omega /(m g)
E. v=\tau \omega /(\mu m g)