Answer
The bungee cord should stretch a distance of 0.602 meters.
Work Step by Step
After falling a distance of 41.0 meters, the potential energy stored in the bungee cord will be equal in magnitude to the person's change in potential energy. Note that the bungee cord will be stretched a distance of 11.0 meters.
$\frac{1}{2}kx^2 = mgh$
$k = \frac{2mgh}{x^2}$
$k = \frac{(2)(95.0~kg)(9.80~m/s^2)(41.0~m)}{(11.0~m)^2}$
$k = 631~N/m$
We can find the distance the bungee cord stretches when we pull on it with a force of 380.0 N
$kx = F$
$x = \frac{F}{k} = \frac{380.0~N}{631~N/m}$
$x = 0.602~m$
The bungee cord should stretch a distance of 0.602 meters.
