World-class downhill ski racers reach speeds up to 150 km/h. The objective of this problem is to estimate the forces on a skier at that speed. For simplicity, the skier will be modeled as two cylinders (legs) attached to a sphere (the rest of the body, including the trunk, arms, and head). Some very approximate dimensions are D = 14 cm and L = 70 cm for each leg and D = 70 cm for the rest of the body. For air at 0 °C, ρ = 1.29 kg/m³ and ν = 1.32 × 10⁻⁵ m²/s.

(a) Calculate the air drag on the skier.

(b) Also resisting the motion is the force on the skis, which is a combination of air drag on them and friction where they contact the snow. Suppose that a skier with a mass of 90 kg is moving at a constant speed down a 45° slope. What fraction of the total resistance is due to the force on the skis?

(c) Modeling each ski as a flat plate of width W = 7 cm and length L = 220 cm that has one side exposed to the air, estimate the air drag. How important is that relative to the friction on the snow?