# Unknown unstretched elastic cord length

1. Dec 3, 2004

### gosbun

A person jumps from a balloon 65m above the ground. He will stop 10m above the ground. A 5m length of the same cord stretches 1.5m with his body weight. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon. What length of cord should the jumper use?

Is the spring or elastic constant (mg/1.5)? If it is how do I set up the equation?

I know that mgyi=65m, and mgyf=10m.

2. Dec 3, 2004

### Staff: Mentor

That's the spring constant for a 5m length of cord; the spring constant is inversely proportional to the cord length.

The key to this problem is energy conservation: The initial gravitational PE is transformed to spring potential energy. (Spring PE is given by $1/2kx^2$.) Realize that both the maximum spring extension (x) and the spring constant are functions of the cord length: Set up the equation and you can solve for that cord length.