\"A spy tries to infiltrate enemy territory by engaging in a low-deployment para

Question

"A spy tries to infiltrate enemy territory by engaging in a low-deployment parachute jump over water. The spy jumps from an airplane, and falls to an altitude of 75 meters, reaching a terminal velocity of 37 m/s by this time. All the values here refer only to vertical direction, and it is only the veritical direction that you need to consider. At this altitude, the spy deploys her parachute, which provides her with an upward net acceleration of 10m/s/s while open. At an altitude X above the water, the spy drops her parachute and freefalls under the acceleration of gravity (9.8m/s/s). The spy will be killed if she enters the water at speeds greater than 15 m/s. Determine X to minimize the time for her parachute to be open and that she will not be killed."

Not even sure how to set this up - I have equations for the first and second sections using

Explanation / Answer

so logically the speed has to be exactly alsmost equal to 15 m/s

let the altitude be X

let the spy velocity at the point of leaving of parachute be v

using V2-U2 = 2aS

v2-372 = 2*-10*(75-X) -------> time during which parachute is on

152-v2 = 2*9.8*(X)   -------> time after which parachute is left

on adding we get

225-1369 = -1500 + 20X +19.6 X

X = 8.98 9meters above water the spy has to leave the parachute

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