Walker, Halliday & Resnick — Force and Motion-II: Problem 40

40 In downhill speed skiing a skier is retarded by both the air drag force on the body and the kinetic frictional force on the skis. (a) Suppose the slope angle is \(\theta = 40.0^\circ\), the snow is dry snow with a coefficient of kinetic friction \(\mu_k = 0.0380\), the mass of the skier and equipment is \(m = 85.0 \text{ kg}\), the cross-sectional area of the (tucked) skier is \(A = 1.30 \text{ m}^2\), the drag coefficient is \(C = 0.150\), and the air density is \(\rho = 1.20 \text{ kg/m}^3\). (a) What is the terminal speed? (b) If a skier can vary \(C\) by a slight amount \(dC\) by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed?