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Question

It's your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 120 m above a raging river and attach a 35-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40 N/m. Assume that your mass is 70 kg. After a long hesitation, you dive off the bridge.

1) How far are you above the water when the cord reaches its maximum elongation?

Answer 1

Initial energy

GPE = 120*9.8*70

KE = 0

SPE = 0 (spring potential energy)

Energy at maximum elongation

GPE = x*9.8*70

KE = 0

SPE = 40/2(120 - 35 - x)^2

Conservation of energy

120*9.8*70 = x*9.8*70 + 40/2(85 - x)^2

82320 = 686x + 20(7225 - 170x + x^2)

82320 = 686x + 144500 - 3400x + 20x^2

20x^2 - 2714x + 62180 = 0

Using the quadratic equation:

x = 29.19 m