# Find the height of an object when a bungee cord stops it

## Homework Statement

Note: A bungee cord can stretch, but it is
never compressed. When the distance be-
tween the two ends of the cord is less than
its unstretched length L0, the cord folds and
its tension is zero. For simplicity, neglect the
cord’s own weight and inertia as well as the
air drag on the ball and the cord.
A bungee cord has length L0 = 34 m when
unstretched; when it’s stretched to L > L0,
the cord’s tension obeys Hooke’s law with
“spring” constant 53 N/m. To test the cord’s
reliability, one end is tied to a high bridge of
height 94 m above the surface of a river) and
the other end is tied to a steel ball of mass
98 kg. The ball is dropped off the bridge with
zero initial speed.
Fortunately, the cord works and the ball
stops in the air a few meters before it hits the
water — and then the cord pulls it back up.
The acceleration of gravity is 9.8 m/s2 .
Calculate the ball’s height above the wa-
ter’s surface at this lowest point of its trajec-
tory.

2. The attempt at a solution

At first I thought maybe this could be solved using Fg= ma and then dividing Fg by the spring constant because at the bottom point Ft should be equivalent to Fg. That didn't work, so I tried setting it up like a conservation of energy problem.

mg(94)= 1/2 k (60-h)^2 + mgh

I solved for h and got 2.3 m. This is also not right. What am I doing wrong here?