A daredevil plans to bungee jump from a balloon 57.0 m above a carnival midway.

Question

A daredevil plans to bungee jump from a balloon57.0m above a carnival midway. He will use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 10.0 m above the ground. Model his body as a particle and the cord as having negligible mass and obeying Hooke's law. In a preliminary test, hanging at rest from a 5.00 m length of the cord, he finds that his body weight stretches it by1.50m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon.

Explanation / Answer

Set up a proportion to determine how long the cord should be.

(stretched test length)/(test length) = (stretched performance length)/(performance length)

Stretched test length = 5 m + 1.5 m = 6.5 m

Stretched performance length = 57 m above ground - 10 m above ground = 47 m

6.5/5 = 47/L
L = 47(6.5)/5 = 36.2 m

Calculate spring constant for bungee cord.

F = kx where F = mg, the weight of the stuntman and x is the distance the test cord was stretched.

mg = k(1.5)
k = mg/1.5

The stuntman will experience gravitational acceleration on the way down, and upward acceleration due to the spring jerking him up from the bottom of his descent.

The force to stretch the spring will snap him upward.

F = kx = ma

x is the distance the spring stretches during performance: 47 - 36.2 = 10.8 meters.

kx = ma

a = kx/m = mg(10.8)/1.5m = 10.8g/1.5 = 7.2g = 7.2(9.8) = 70.56 m/s2

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