A skydiver weighing 180lb (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 of $12|v|$ when the parachute is open, where the velocity $v$ is measured in ft/s.

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 $v_L$ after the parachute opens?

Question

A skydiver weighing 180lb (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 of $12|v|$ when the parachute is open, where the velocity $v$ is measured in ft/s.

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 $v_L$ after the parachute opens?