MTHSC 360 – Three Linked Bungee Jumpers
January 25, 2008
1
The Basic Problem
Three Bungee jumpers  Alex, Barry, and Carol  plan to form a single long bungee cord by tying
themselves together with three short bungee cords and then jump off a bridge. That is, the first
jumper, Alex, is tied to the bridge by a bungee cord, the second jumper, Barry, is tied to Alex with
a second bungee cord, and the third jumper, Carol, is tied to Barry with a third bungee cord. Our
goal is to determine the final positions of the three jumpers.
Let
z
A
,
z
B
, and
z
C
denote the distance below the bridge for Alex, Barry, and Carol, respectively.
The distances will be measured in feet and the time will be measured in seconds.
The distance
will be a positive number as long as the jumper is below the bridge. Assume that the weights of
the three jumpers are:
w
A
= 225 lbs,
w
B
= 160 lbs, and
w
C
= 105 lbs, respectively.
Assume
that each of the short cords is 15 feet long. Furthermore, assume that the behavior of the bungee
cords is similar to idealized springs, in that the restoring force is proportional to the amount that
the cord has been stretched, and assume that the proportionality constants are
c
1
= 75 lbs/ft and
c
2
=
c
3
= 30 lbs/ft, respectively. Finally, assume that the weights of the bungee cords are negligible.
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 Spring '08
 Warner
 Force, bungee cord, Bungee jumping

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