Bungee Jumping: Solving for Mass, Cord Length, and Period of Oscillations

[sona1177]

Homework Statement

A bungee jumper leaps from a bridge and undergoes a series of oscillations. Assume g=9.78 m/s^2. If a 58.0 kg bungee jumpers jumps from length of 20.0 m and she jumps from a heigh of 66.0 m above the river, coming to rest a few centimeters above the water surface on the first downward descent. What is the period of the oscillations? Assume the bungee cord follows Hooke's Law. The next jumper in line has a mass of 88.0 kg. Should he jump using the same cord?

A) kx - mg= 0

k=mg/x
k= (58.0 * 9.78)/46
k=12.33
w= sq rt (k/m)=sq rt (12.33/58.0)=.4611
w=2pif
w=2pi/T
T = (2pi)/w
T=(2pi)/.4616
T=13.6 seconds

B) kx -mg =0
kx=mg
x=mg/k
(88.0 * 9.78)/12.36=69.6

No, he should not jump using the same cord b/c the cord will stretch and he will not be able to avoid the water.

These answers are wrong and I don't see why.

Homework Equations

The Attempt at a Solution

 

[barthayn]

x is not 46 metres. It is 20 metres because the x stands for how much it stretched. If that doesn't work, try 1/2kx^2.

46 metre is the normal length of the rope.