Bungee Jumping Maths

  • #1
Hi, the following questions are sorta both a physicy/mathsy questions however since I only do maths c (and have never done physics) any mathematical explanations would be greatly appreciated.

p.s. I came across this question on the internet and am quite interested in this kind of stuff, however I really do not have any idea how to do any of it, or where to begin. So even if someone helps starts me off or gives me an idea of how to solve them that would be great!

Thanks in advance!

:New Zealand is the home of bungee jumping. One of the major jumps is located on a bridge over the Shotover River near Queenstown.
In this case, the bridge is 71 m above the river.
Two types of jumps are available — wet and dry. In a dry jump, the person’s fall ends just above the water surface. In a wet jump the person is submerged to a depth of 1 m.
Participants jump from the bridge, fastened to an elastic rope that is adjusted to halt their descent at an appropriate level.
The rope is specially designed and its spring constant is known from specifications. For the purposes of the problem, we will assume that the rope is stretched to twice its normal length by a person of mass 75 kg hanging at rest from the free end. It is necessary to adjust the length of the rope in terms of the weight of the jumper.

1. For a person of mass m kg, calculate the depth to which a person would fall if attached to a rope of the type described above, with length l metres. Treat the jumper as a particle so that the height of the person can be neglected. Discuss the assumptions made in this calculation.

2. If you were the person jumping off the 71 m attraction, find the length of rope needed for a dry jump, where the descent is halted 1 m above the water.

3.Now find the length of rope needed for a wet jump, where the descent would end 1 m below the surface of the water. Find the speed of entry to the water.

4.In practice, the bungee rope is attached to the ankles of the jumper. Refine the previous model to allow for the height of the jumper and modify the earlier calculations. Is the difference significant?
 

Answers and Replies

  • #2
This thread should go to the homework section.

Look for "Hooke's Law".
Look for "Weight".
Look for "Newton's second law".
Look for "Free fall".
Look for "Free body diagram" and draw diagrams for each jump phase: before jump, free
fall until the rope starts to stretch, fall between the rope stretching and the water.
Look for "Free fall in Newtonian mechanics"

How can you relate Newton's second law, Hooke's law and weight ?
Can you tell the expression for fall time, velocity or rope length applying Newtonian mechanics ?
 

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