What is the Conservation of Energy Principle in Bungee Jumping?

[jasonbans]

Homework Statement

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.

Homework Equations

Ek=1/2mv^2
Ep=mgh
Ee=1/2kx^2

The Attempt at a Solution

so i did mgh = 1/2mv^2 + 1/2kx^2 and solve for v but somehow i am not getting the answer 6.3m/s

 

[PeterO]

Homework Statement

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.

Homework Equations

Ek=1/2mv^2
Ep=mgh
Ee=1/2kx^2

The Attempt at a Solution

so i did mgh = 1/2mv^2 + 1/2kx^2 and solve for v but somehow i am not getting the answer 6.3m/s

You may have substituted in some incorrect values, or you may have "mis-used" you calculator.

Show us your substitution / simplifications so we can see what went wrong.

 

[jasonbans]

this is what i did

 

[PeterO]

this is what i did

Two problems:

When 12.5 m above the water, the jumper has not descended 48m, so you h value is not appropriate, and the bungee has not been stretched 12.5 m, so your x value is not appropriate.

 

[jasonbans]

12.5 above the water meaning 48 subtract 12.5 = 35.5m for the height?
i don't know how much it stretched by am i suppose to calculate it?

 

[jasonbans]

thx got the answer now

 

[PeterO]

is the height 35.5 m and it stretched 25.5m right?

if it was 10.0 m long to start with it will have stretched 25.5m

edie: the h value is 35.5, yes. best called the change in height.