A skydiver weighing 180 pounds jumps from a height of 5000 feet. Calculate the drag coefficient for the open parachute so that terminal velocity is no greater than 21 ft/s. Neglect drag when the chute is closed. At what height must the parachute open his parachute so he doesn't an hero?
No diff eqs are necessary. At terminal velocity, the guy's in equilibrium.
However, it takes an infinite distance for him to reach terminal velocity... so what's the fastest speed he can hit the ground without an hero'ing? Unless he opens the parachute before he reaches 21 ft/s ~ 7 m/s, which gives him about a second of skydiving fun.
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Anonymous2009-02-20 3:54
set skydiver weight equal to drag and solve for coefficient, blah blah.
second part harder. make a piecewise function of your velocity, first interval is before you pull shoot(just gravity acting), second is after (gravity minus air resistance). air resistance is based on instantaneous velocity, so you'll need to solve a quadratic or something for that part.
integrate dh/dt over some unknown interval and set the integral equal to 5000, solve for maximum point of release such that your velocity at the end point is 21 ft/s and the integral is equal to 5000.
dont listen to me, i'm just talking out of my ass, i dont know the actual way to do this, i just made that up cause it sounded good in my head.