- #1

Furby

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**Bungee Jump--Springs and Energy**

## Homework Statement

A person bungee jumps off a bridge.

The person's mass is 90kg.

The height of the bridge above the water is 80m.

The bungee chord has a length of 25m.

The bungee chord's spring constant is 30 N/m.

What is the minimum distance the person will be from the surface of the water?

## Homework Equations

PE

_{s}=1/2*k*x

^{2}

PE

_{g}=m*g*h

## The Attempt at a Solution

I assigned the point of jump at the height of the bridge as y=0, thus as the jumper falls his PE

_{g}increases, becoming more negative. Kinetic energy is growing at the same rate until 25m, the chord's equilibrium point, where the chord will begin to stretch and exert a force on the jumper opposite to gravity.

Afterwards the kinetic energy begins to convert to PE

_{s}always growing in equal value to the constantly increasing PE

_{g}. Thus at the end, or 'bottom' of the person's jump, he will no longer have any KE, and thus:

mgh=1/2*kx

^{2}

h=25+x

Use some algebra and you get a quadratic:

15x

^{2}-882x-22050=0

x=77.715m

Which add the initial 25m and you get 102m, obviously exceeding the 80m height. The bungee jumper would then easily hit the water. I solved the problem another way assigning y=0 at the point of greatest KE (25m) and set PE

_{g}to be 0 at this point as well, and received the same answer.

My first assumption is that there was a typo and the problem is intended to have a 300 N/m spring constant, but I'm curious to see if I did anything wrong?