Work Step by Step
The correct way to think about it is in terms of energy: the skier’s initial gravitational potential energy is converted into kinetic energy at the bottom. Therefore, the skiers starting from higher up have the greatest speed when they reach the bottom. The question is how to decide between the latter 2 cases when friction is acting. An analysis shows that the friction on the steeper slope is smaller in magnitude than on the flatter slope. The normal force from the hill is smaller, and the friction is proportional to that. In an extreme limit, for a vertical hill the contact force is zero and friction will be zero. Furthermore, on the steeper slope in C, the friction acts over a shorter distance. Conclusion: the skier will be traveling faster in case C than in any of the other cases.