Maximum speed of car on downhill

[Jack122]

Homework Statement

The exercise is this: The mass of the car is m=500 kg. The maximum speed of the car on flat road is v1=35 m/s and on 10 % up hill (tan(alpha)=0.1, alpha is with respect to flat) the maximum speed is v2=20 m/s. The friction force is double on up hill because it has been made with different material. What is the maximum speed of the car on down hill (5%) when the road is made with the same material than the flat surface? Suppose that the air resistance is zero.

Homework Equations

P=F*v
Gx=mg sin(alpha)
F_f=friction force

The Attempt at a Solution

I think the exercise itself is not correct. The power of the car on flat is P1=(F_f)v1 and on up hill it is P2=(2(F_f)+mg sin(alpha))v2. The powers need to be the same. So when I solve for F_f I get F_f=(mg sin(alpha)v2)/(v1-2v2) and this is smaller than zero because v1-2v2=(35-2*20) m/s=-5 m/s and mg sin(alpha)v2 is greater than zero (sin(alpha)=sin(arctan(0.1))=0.0995). But the friction force needs to be greater than zero. So I think this is incorrect exercise because the car cannot produce enough power to climb that hill with that speed.

 

[haruspex]

I agree with you. Maybe it meant to say the friction is double on the flat?

There is another reason the question is nonsense. Friction between road and tyre does not impede the progress of the vehicle. In the present case that is static friction. No work is required to overcome it. Indeed, without it the hill could not be climbed. Presumably the question means rolling resistance, not friction.