A ball of mass m is thrown vertically upward with a speed of v_{0}. The ball is subject to an air resistance force that is proportional to the velocity, F=-k v. The ball rises up to height of h and then returns to the starting point after some total time t_{f}. The acceleration of free fall is g.
Determine the following:
a. An expression for the velocity as a function of time in terms of any or all of the constants.
b. Sketch the graph of velocity vs time. On the sketch indicate the time to rise to the highest point, t_{r}, and the total time of flight, t_{f}. You do not need to find either t_{r} or t_{f} at this point, but your graph should reflect relative positions of both.
c. Find the time to rise, t_{r}, to the highest point, h, in terms of any or all of the constants.