# Simulation : Skydiver in Free-fall

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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.

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##### Solution Summary

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.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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