Max Speed Homework Solution - Find Maximum Speed

[Mmm_Pasta]

Homework Statement

The Royal Gorge bridge over the Arkansas River is 310 m above the river. A 64-kg bungee jumper has an elastic cord with an unstressed length of 63 m attached to her feet. Assume that, like an ideal spring, the cord is massless and provides a linear restoring force when stretched. The jumper leaps, and at at her lowest point she barely touches the water. After numerous ascents and descents, she comes to rest at a height h above the water. Model the jumper as a point particle and assume that any effects of air resistance are negligible.

I need to find the maximum speed which is 46.9 m/s.

Homework Equations

I used:

F=-kx
KE=1/2mv²
GPE=mgh
EPE=1/2kx²
F=ma

The Attempt at a Solution

I found k; k=6.38. Using k I found the force of the cord at the bottom. 6.38 N/m(247 m) = 1575.86 N, subtract 627.84 N because this is the force of gravity; force of the cord is 948.02 N. Using F=ma, I found the acceleration of the cord to be 14.81 m/s². I know that to find the maximum speed I have to find where the force of the cord is equal to the force of gravity because this is the point where the jumper begins to slow down. This is the part I need help with.

 

[Tusike]

Where she's not accelerating anymore, that's where the force of the cord will be equal to the force of the gravity. Does the problem mention any place where she's moving at a constant speed or just not moving?

 

[Mmm_Pasta]

After she goes up and down a few times she does remain at rest which is at 149m. When I use 149m to solve for speed, it does not work. I derived 198m as the maximum speed height, but I don't know how that is figured out without speed.

 

[Tusike]

"she comes to rest at a height h above the water"

How did you know that h=149m? Supposing the problem gave that information as well, this means that at this point the cord is stretched (310-149-63) = 98m, and the jumper has fallen a height of 310-149=161m. Work done = energy change, so it should be fairly simple from here if you know the cord's constant D (or k or whatever you called it).

 

[Mmm_Pasta]

I have it now, thank you.