Final answer:
The coefficient of kinetic friction when Jane rides down a slope at a constant speed is found by setting the component of gravitational force down the slope equal to the force of kinetic friction. The answer is (C) μ = tan θ.
Step-by-step explanation:
To determine the coefficient of kinetic friction between the sled and the slope when Jane rides down at a constant speed and neglecting air resistance, we use the principle that the net force acting on the sled must be zero for it to maintain constant velocity. The two main forces acting on the sled are the component of gravitational force down the slope, which is mg sin θ, and the force of kinetic friction, which is μmg cos θ. Since these forces must be equal in magnitude and opposite in direction for the sled to have zero acceleration, we set them equal to each other:
mg sin θ = μmg cos θ
By dividing both sides of the equation by mg cos θ, we find the coefficient of kinetic friction μ:
μ = tan θ
Therefore, the correct answer is (C) μ = tan θ.