Chapter 1.1, Problem 12E

The velocity u of a freefalling skydiver is well modeled by the differential equation
   $m\frac{dv}{dt}=mg-k{v}^2$
where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position of the diver during the dive. (Note that the constants m, g, and k are positive.)
(a) Perform a qualitative analysis of this model.
(b) Calculate the terminal velocity of the skydiver. Express your answer in termsof m, g, and k.