Consider a skydiver (mass m) jumping out of a plane. let the downward direction be the positive direction for position x(t) of the skydiver at time t (as measured from the plane located at x = gravity exerts a downward force on the skydiver farav = mg, where g is the constant acceleration due to gravity. air resistance exerts an upward force (which increases as the velocity increases), given by fair = -av, where a > 0 is the drag coefficient
(a) use newton's second law to derive a de model of this problem, with dependent variable x
(b) find the general solution of the de in part (a)
(c) given initial position and velocity r(0) = 0 and x'(0) = v0, find the solution of the ivp.
(d) find the velocity v = x' of your answer from part (c) and graph it on a v vs. t plot for vo = 0.
(e) what is the long-term behavior of the velocity (i. e., lim v( give a physical interpretation too