PhysicsLAB: 2008 C1

A skier of mass M is skiing down a frictionless hill that makes an angle θ with the horizontal, as shown in the diagram. The skier starts from rest at time t = 0 and is subject to a velocity-dependent drag force due to air resistance of the form F = -bv, where v is the velocity of the skier and b is a positive constant. Express all algebraic answers in terms of M, b, θ, and fundamental constants.

	(a) On the dot below that represents the skier, draw a free-body diagram indicating and labeling all of the forces that act on the skier while the skier descends the hill.

	(b) Write a differential equation that can be used to solve for the velocity of the skier as a function of time.

	(c) Determine an expression for the terminal velocity v_T of the skier.

	(d) Solve the differential equation in part (b) to determine the velocity of the skier as a function of time, showing all your steps.

	(e) On the axes below, sketch a graph of the acceleration a of the skier as a function of time t, and indicate the initial value of a. Take downhill as positive.