a)Assume the net slows him down with constant deceleration. If a human can handl

Question

a)Assume the net slows him down with constant deceleration. If a human can handle a maximum forwards acceleration of about 20g and a maximum backwards acceleration of about 6g for up to 10 seconds, what is the minimum height the net must be off the ground if he lands on his back? If the deceleration of the net is not constant how would this change your answer? If the net is at this minimum height, for what length of time is the net slowing him down?

b)Based on the first 30 seconds of data, how long did he fall before he hit the net?

In August 2016 skydiver Luke Akins jumped from a height of 25,000 feet without a parachute. He landed safely in a 100x100 net. The graph below shows his height for the first 30 seconds of his skydive. Height versus time 25000 24 000 23000 22 000 21000 20000 10 15 20 25 30 time (s)

Explanation / Answer

a. assuming, the net slows him down with constant deceleration

maximumj possible deceleration ( that can be taken by humans) = a = 6g

time, t = 10 s

height of net from ground = h

velocity ( terminal velocity) of the diver just be contact = v

from the graph we can see v is constant and equals the slope of the graph towards the end

v = (20,000 - 2400)/(30 - 8) = -181.8181 ft/s = 55.418 m/s

so assuming constant deeceleration

let time taken be t' for the man to come to a halt

then

2*a*h = v^2

h = 55.418^2/2*6g = 26.088 m

time taken to slow him down = t'

v = at

55.418 = 6g*t'

t' = 0.9415 s

b. based on the data from the chart, net time be t

then t = 8 + 24,000 ft / v = 8 + 24,000/181.8181 = 140 s

here we have taken first 8 seconds as itr is, and after that we have assumed the diver falls with constant velocity of v which is its terminal velocity as seen from the graph

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