Final answer:
To maintain a constant speed, the skier must exert a force equal to the kinetic friction. This is calculated by multiplying the coefficient of kinetic friction by the normal force, leading to a required force of approximately 108.79 N.
Step-by-step explanation:
The question asks to calculate the force a cross-country skier must exert to move at a constant speed on snow, accounting for the coefficient of kinetic friction. To maintain a constant speed, the skier must exert a force that is equal to the force of kinetic friction acting against him. This force can be calculated using the formula f_k = μ_k × N, where f_k is the force of kinetic friction, μ_k is the coefficient of kinetic friction, and N is the normal force (which, on flat ground, is equal to the weight of the skier, mg).
In this scenario, the skier's weight is mg = 84.7 kg × 9.8 m/s2 = 830.46 N. The force of kinetic friction would thus be f_k = 0.131 × 830.46 N ≈ 108.79 N. Therefore, to move at a constant speed, the skier must exert a force of approximately 108.79 N against the snow.