Answer
The minimum spring constant of the bungee cord is $113~N/m$
Work Step by Step
Jorge needs to stop a distance of 53.0 meters below his starting point. Thus the bungee cord needs to stretch a distance of 26.0 meters. The change in gravitational potential energy will be equal in magnitude to the elastic potential energy stored in the bungee cord at the bottom of the jump:
$\frac{1}{2}kx^2 = mgh$
$k = \frac{2mgh}{x^2}$
$k = \frac{(2)(75.0~kg)(9.80~m/s^2)(53.0~m)}{(26.0~m)^2}$
$k = 113~N/m$
The minimum spring constant of the bungee cord is $113~N/m$.
