Question

The maximum torque output from the engine of a new experimental car of mass m is τ. The maximum rotational speed of the engine is ω. 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 µ.
What is the maximum sustained speed v the car can drive up a 30 degree incline? Assume no frictional losses and assume µ is large enough so that the tires do not slip.

Answer 1

Normal force = m g cos 30
max friction force = mu m g cos 30

power in = power out
P = (mu m g cos 30) v

Answer 2

It says that mu is large enough that the tires don't slip
the answer is v = 2P/mg
of why there is not root(3) in the denominator i am not sure but that is what the USAPho test solution says.