Question

a 60 kg daredevil physicist attaches a bungee cord with a force constant of 15.5 N/m to his waist and jumps
off a bridge that is 100 m above the water. The unstretched length of the bungee cord is 8.0 m.
a. Calculate his speed when he is half way down.
b Does he hit the water? Calculate how far he jumps.

Answer 1

Answer on Question #70771-Physics-Other

A 60 kg daredevil physicist attaches a bungee cord with a force constant of 15.5 N/m to his waist and jumps off a bridge that is 100 m above the water. The unstretched length of the bungee cord is 8.0 m.

a. Calculate his speed when he is half way down.

b Does he hit the water? Calculate how far he jumps.

Solution

a.

$$\frac{mgh}{2} = \frac{mv^2}{2} + \frac{k}{2} \left(\frac{h}{2} - x\right)^2$$ $$v = \sqrt{gh - \frac{k}{m} \left(\frac{h}{2} - x\right)^2} = \sqrt{(9.81)100 - \frac{15.5}{60}(50 - 8)^2} = 22.9 \frac{m}{s}.$$

b. At the water:

$$mgh = \frac{mv^2}{2} + \frac{k}{2} (h - x)^2$$ $$mgh = 60(9.81)100 = 58860 \, J.$$ $$\frac{k}{2} (h - x)^2 = \frac{15.5}{2} (100 - 8)^2 = 65596 \, J > 58860 \, J.$$

Thus event at zero speed daredevil physicist cannot hit the water.

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