Bungee Jump

How far does the cord stretch, how hard does it pull at the bottom, and how long a cord is still safe? The energy of the fall is caught by the elastic cord like a giant spring.

Machine elementsEnergyJust for fun

Inputs

Input examples

The jumper falls freely for the length of the cord, then the cord stretches like a spring until all the energy is stored. Air drag and the jumper’s own height are ignored.

Height of the platform above the ground

Unstretched cord length L

Cord stiffness k

Jumper mass

Safety margin above the ground

Catching a Fall

For the first stretch of the jump the cord is slack and you are in free fall. Once it is taut it acts like a spring, slowing you down until all the energy of the fall is stored in the stretched cord — then it throws you back up.

The worst moment is the bottom: the cord pulls hardest there, typically 2–3 g. A heavier jumper stretches the same cord much further, so operators pick the cord for each person’s weight. Real cords also have damping, which shrinks every rebound.

mg(L+x)energy of the fall

½kx²stored in the cord

2–3 gat the bottom

heaviermuch deeper

Height During the Jump

first bounce

jumper height

cord starts to stretch

ground

Result

Enter the values above

Key Relations

Lowest Point

All the potential energy lost over the fall L + x ends up in the stretched cord; solve the quadratic for the stretch x.

Example:

Fastest Point

You keep speeding up until the cord pulls as hard as gravity, at a stretch of mg/k.

Peak Pull

The net upward acceleration at the bottom, often given in g.

Sources & Verification

References

D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 8 (Potential Energy and Conservation of Energy) and Ch. 15 (Oscillations).