bungee jumper?

Question

a 60kg bungee jumper jumps from the same height as the fixed end of a 10m bugee cord of ks = 200N/m. If g = 10m/s^2 what is the maximum extension of the cord.

Assume cord obeys hookes law, ignoring friction and air resistance. And considering the energy of the system: person + cord.

The answer is 11.3m but I'm having trouble getting it.

Edward, the change in gravitational potential is more than you've put because the bungee stretches after 10m so the potential energy carries on converting.

Answer 1

let us choose displacement (extension =x) so that when
------------------------------------- jumping point h = 10 m
..
================= x=0, origin (unstretched)

====================== x = - x (extension)
energy conservation >> before = after
mg h = - mgx + 0.5 kx^2
0.5 kx^2 - mgx - mg h =0
x^2 - (2mg/k) x - (2mg/k) h =0 -------- (1)
let p = 2mg/k = 2*60*10/200 = 6
x^2 - 6 x - 6*10 =0
x = [6 +- {36+240}^1/2] / 2
x = [6 +- 16.61] / 2
x1= 22.61/2 = 11.305 m >>>>>>>>>>>>>>>
x2 = - ve root (reject)

Answer 2

Ke=Pc
Ke= Pe
Pe=Pc
Pe= mgh
Pc=0.5 k x^2

x=sqrt (2mgh/k)
x=sqrt(2 x 60 x 9.81 x10/200)
x=7.7 m

Good point Lee W
Good job Anilbakshi

Yes the total Potential energy is
Pe= mg(10 + x)=0.5k x^2
then
x^2 - (2mg/k)x - (20mg/k)=0
then x1= [2mg/k + sqrt((2mg/k)^2 + 80mg/k)]/2
x1= [2(60) 10/200 +sqrt(2 x60 x10/200)^2 + 80 x 60 x 10 / 200)]/2

x1= [ 6 + sqrt( 36 + 240)]/2
x1= 11.3 m

Answer 3

yeah, Touching your embassage, return and say, That we with England won't enter parley, Nor on no account make honest climate, or take truce; yet burn their neighbor cities, and so follow prepared Rods previous their city York. and on no account shall our bonny riders relax