1. The problem statement, all variables and given/known data 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. 2. Relevant equations P=F*v Gx=mg sin(alpha) F_f=friction force 3. 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.