How high will UT bounce on a bungee jump from the Golden Gate Bridge?

[Superman123]

1. Ut will bungee jump from the golden gate bridge. The height that she will jump from is 65 meters. The rope pulls her up 8 meters above the water. If UT's weight is 63 kg, how far will the rubber rope pull her upwards, if there's no loss to friction or air resistance?

Homework Equations

PE= mgh
v=√2gh
v^2-u^2=2as

3. The Attempt at a Solution
I started by calculating the energy of the fall.
PE= 63*(65-8)*9.8= 35191 J

I then tried to calculate the velocity that she reaches when she is about to fall.
v=√2gh= 33.45 m/s

I then used v^2-u^2=2as, u^2 at the top is 0 and a= g=9.8 and s=h
v^2-u^2=2as
33.45^2-0= 2*9.82* s
s= 55.4 meters

That seems oddly wrong that she could reach such a height, is this the right way to do it or is there a mistake?

 

[PeroK]

What happens if literally no energy is lost?

 

[Superman123]

Well, the energy produced will be enough to bounce her back where she started, if nothing of it is lost; though I don't know how to present it with formulas to show that my reasoning is enough

 

[PeroK]

Well, the energy produced will be enough to bounce her back where she started, if nothing of it is lost; though I don't know how to present it with formulas to show that my reasoning is enough

I would say you don't need any formulas, but you perhaps need to describe the scenario in physics terms. After all, if you push a vehicle along a flat, frictionless track, it doesn't come back to where it started.

 

[Superman123]

Is saying " The energy of the fall will be preserved in the rope and because there's no energy loss, the rope will pull up UT with the same energy, getting here to the same she started in." correct, considering physics terms?

 

[PeroK]

Is saying " The energy of the fall will be preserved in the rope and because there's no energy loss, the rope will pull up UT with the same energy, getting here to the same she started in." correct, considering physics terms?

Perhaps better is that the initial gravitational PE is converted to elastic PE in the rope, then back to gravitational PE again ...

 

[Superman123]

Oh, thanks for your time and help!