A sky diver, weighing M Kg, jumps from a moving aircraft at X meters above the ground. He/She initially free-falls for a period of seconds then deploys a parachute to to allow him/her to land at a safe speed of under 6 m/s.
The sky diver uses a spread-eagle position during freefall that maximises their drag coefficient , Cd. (Cd based on frontal area of 0.5m2)
Full parachute deployment takes 5 seconds and during this period the drag coefficient of the parachute can be assumed to vary linearly between 0 and the final value needed for a safe descent speed.
Using whatever numerical techniques appropriate determine a velocity versus time graph of his/her descent. Estimate the amount of free fall time that would be possible that would still allow full deployment of the parachute and a safe landing. Ignore any initial horizontal velocity of the aircraft and wind or atmospheric turbulence conditions.