How Do You Calculate the Speed of a Bungee Jumper 19m Below the Launch Point?

[BlueCardBird]

Homework Statement

A bungee jumper of mass 75 kg is standing on a platform 53m above the river. The length of the unstretched bungee cord is 11m. The spring constant of the cord is 65.5N/m. Calculate the jumpers speed at 19m below the bridge on the first fall.

Homework Equations

Em1=Em2 Ek=1/2mv^2 Es=1/2kx^2 GPE=mgh

The Attempt at a Solution

Find x by subtracting 11m from 19m which is 8m, this is how far the bungee cord is stretched. Use x in formula gpe=Ek+Es. Problem arises when I sub values in answer is off.

 

[Chestermiller]

Show us what you did.

 

[BlueCardBird]

x=19m-11m
mgh=1/2mv^2+1/2kx^2
subbed values in but didnt get right answer :S

 

[Chestermiller]

What did you use for h?

 

[BlueCardBird]

Height of the cliff or bridge which is 53m

 

[Chestermiller]

That's your problem. He hasn't fallen the whole distance yet. He has only fallen h = 19 m.

 

[BlueCardBird]

wait but total energy at top of the cliff is mgh where height is 53 m though

 

[Chestermiller]

Try 19 m in your equations and see what you get. The equation should be mgΔh. It is the change in potential energy that matters, not the total potential energy relative to some arbitrary reference.