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ThreeBungeeJumpers

# ThreeBungeeJumpers - MTHSC 360 Three Linked Bungee Jumpers...

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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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ThreeBungeeJumpers - MTHSC 360 Three Linked Bungee Jumpers...

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