At what angle should a ski run be chosen for a skater wanting to maintain a constant speed on a snowy slope with a given friction coefficient?

To maintain a constant speed while skiing down a slope, the forces acting on the skier must be in equilibrium. This means that the gravitational component pulling the skier down the slope must be balanced by the frictional force opposing the motion.

When a slope is inclined at an angle, the gravitational force acting on the skier can be decomposed into two components: one that acts parallel to the slope (which causes the skier to accelerate down) and the other that acts perpendicular to the slope (which affects the normal force and, in turn, the friction). The angle at which these two forces achieve equilibrium relies on the coefficient of friction between the skis and the snow.

For a specific coefficient of friction, there exists a precise angle at which the downhill force component is equal to the frictional force. This angle allows the skier to maintain a constant speed because the net force acting on them becomes zero. Choosing this angle ensures that the skier does not accelerate up or down the slope but rather maintains a steady state.

The fact that this specific angle is given as exactly 2.8 degrees indicates that it is derived from the formula considering the friction coefficient. If the angle is set too low, the skier will gain speed due to more gravitational pull, while a steeper