Bungee Jumping!

1. The problem statement, all variables and given/known data

The ##m = 75kg## man jumps off the bridge with ##v_1 = 1.5 m/s##. Determine the unstretched length ##l_0## of the cord in order that he stops momentarily above the surface of the water. The stiffness is ##k = 80 N/m##.

Picture: http://ift.tt/1p7eCZo

2. Relevant equations

3. The attempt at a solution

This is one of those problems they don’t give the answer for and I’m wondering if this is okay.

I drew my FBD stick figure with the Datum plane located through position A. I then used conservation:

##T_1 + V_1 = T_2 + V_2##

Since I stuck the datum plane at the top where the man is, he currently posses no potential energy at all, only kinetic.

In the final phase, the man has lost all of his kinetic energy and it is now in the form of potential. So we have:

##\frac{1}{2} (75) (1.5)^2 + 0 = 0 – (75)(9.81)(150) + \frac{1}{2} (80) (150 – l_0)^2##

Which is quadratic in ##l_0##. Solving I obtain ##l_{0_1} = 203m##, which makes no physical sense at all since it exceeds the jumping height. ##l_{0_2} = 97.5m##, which seems reasonable.

Does this look okay?

http://ift.tt/1lCUsqV

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