A tall bald student (height 2.1 motors and mass 97.4 kg) decides to try bungee j

Question

A tall bald student (height 2.1 motors and mass 97.4 kg) decides to try bungee jumping from a bridge. The bridge is 36.7 motors above the river and the "bungee" is 25.3 motors long as measured from the attachment at the bridge to the foot of jumper. Treat the "bungee"" as an ideal spring and the student as a 2.1-motor rod with all the mass at the midpoint. This particular student desires to stay dry. What is the minimum spring constant (N/m) of the "bungee"' that will allow the student to got as close as possible to the water but still stay dry? Assume that he begins at a standing position and "falls" from the bridge.

Explanation / Answer

For the student to just touch the water, max. extension in the spring = 36.7 - 2.1 - 25.3 = 9.3 m PE of the student turns to PE of the spring mgh = 1/2 kx^2 97.4 * 9.8 * 36.7 = 1/2 * k * (9.3)^2 k = 810 N/m

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