Question

In the dangerous “sport” of bungee-jumping, a daring student jumps
from a balloon with a specially designed elastic cord attached to his
ankles. The unstretched length of the cord is 25.0 m, the student
weighs 700 N, and the balloon is 36.0 m above the surface of a river
below. Assuming that Hooke’s law describes the cord, calculate the
required force constant if the student is to stop safely 4.00 m above
the river.

Answer 1

4.00 m above the river surface, the bungee length is 32 m and it has stretched 7.0 m.
The stored potential energy in the cord is then
PEmax = (1/2)k*7^2 . This equals the gravitational potential energy loss, M*g*32. Kinetic energy at the top and bottom of the jump is zero.
(49/2)k = 32 M g
Solve for k.