A skydiver, weighing 70kg, jumps from an aeroplane at an altitude of 700 metres and falls for (T) seconds before pulling the rip cord of his parachute. A landing is said to gentle if the velocity on impact is no more than the impact velocity of an object dropped from a height of 6 metres. The distance that the skydiver falls during (t) seconds can be found from Newton's Second Law, F = ma. During the free fall portion of the jump, we will assume that here is essentially no air resistance, so F = -mg, where
g = 9.8m/s and m = 70kg. After the parachute opens, a significant drag term due to air resistance of the parachute affects the force (F), causing the force to become F = -mg - kv, where (v) is the velocity and
k = 110kg/sec is a drag coefficient.
i. Find the range of times (T) at which the rip cord can be pulled for a gentle landing.
ii. Find the height after (T) seconds of free-fall.
The range of times at which a rip-cord could be pulled to ensure a gentle landing are calculated. Height at different times is als calculated. The solution is detailed and well-presented. A diagram is included.