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A guy, seeing a gold bar on the ground of his high-rise building, rushed out of his window at height .

A guy, seeing a gold bar on the ground of his high-rise building, rushed out of his
window at height . Having taken “Calc IV”, he is smart enough to bring a parachute, yet, he
won’t open it until he absolutely has to. Opening it too early will slow him down while opening it
too late will kill him. If his touchdown speed is smaller than v0 , he can stay alive to spend the bar
to fix his broken bones (hopefully enough). During the fall, his air drag coefficient is k with
parachute closed and nk with it open. The air drag force is also proportional to the falling speed.
At what height the guy should open his parachute so that he can reach the bar quickest and stay
alive? Compute the total falling time.
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