A skydiver, weighing 180 lb (including equipment) falls vertically downward from an altitude of 5000 ft and opens the parachute after 10 s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.75|v| when the parachute is closed and is of magnitude 10|v| when the parachute is open, where the velocity v is measured in ft/s. (A computer algebra system is recommended. Use g = 32 ft/s^2 for the acceleration due to gravity. Round your answers to two decimal places.)
(a) Find the speed of the skydiver when the parachute opens.
(b) Find the distance fallen before the parachute opens.
(c) What is the limiting velocity vL after the parachute opens?
(d) Determine how long the sky diver is in the air after the parachute opens.
(e) Plot the graph of velocity versus time from the beginning of the fall until the sky diver reaches the ground.