# Energy problem on bungee jumper

1. Oct 16, 2004

### decamij

I'm having trouble solving this problem. can n e one help me?

A bungee jumper of mass 64.5 kg (including safety gear) is
standing on a platform 48.0 m above a river. The length of
the unstretched bungee cord is 10.1 m. The force constant
of the cord is 65.5 N/m. The jumper falls from rest and just
touches the water at a speed of zero. The cord acts like an
ideal spring. Use conservation of energy to determine the
jumper’s speed at a height of 12.5 m above the water on
the first fall.

I used the work equation to find the total energy, then subtracted the elastic potential energy and gravitational potential energy at 12.5m above ground. Then i solved for Ek, and used THAT equation to solve for speed.
i got 9.29m/s, but the answer is 6.37m/s.

What did i do wrong?

2. Oct 16, 2004

### neutrino

What were the numbers that you put into the term for elastic potential energy?

3. Oct 16, 2004

### decamij

elastic potential energy is E = 0.5 kx^2, right?

I put: k = 65.5, x = 35.5 FIRST, but then i ended up getting a negative answer, so i used x = 12.5.

But is what i tried to do correct, did i miss anything? I'm starting to think that i calculated the total energy wrong. What did you get for total energy?

4. Oct 16, 2004

### Staff: Mentor

Correct.
Both x = 35.5 m and x = 12.5 m are wrong. How much is the cord stretched (beyond its unstretched length) when the jumper is 12.5 m above the water?

5. Nov 1, 2004

### pmrazavi

you should find the "delta X", by this equation: mgh=.5kx^2, I got 30.45 m for delta X,
then you should put this value in the equation: mgh=.5kx^2+mgh`+.5mv^2 and find the velocity..the initial X, 10.1, is extra in the given problem.