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Question

# As part of a physics open house, a department sets up a bungee jump from the top of the physics building. Assume that one end of the elastic band will be firmly attached to the top of the building and the other to the waist of a courageous participant. The participant will step off the edge of the building, to be slowed down and brought back up by the elastic band before hitting the ground. Estimate the length and spring constant of the elastic you would recommend.

Solution

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## Concept

Let us suppose that the height of the building is $\color{#c34632} y$. For the maximum expirience it is best to make an elastic band with unstretched length $\boxed{\color{#4257b2}L=\dfrac{y}{2}}$ and choose the spring constant $\color{#c34632} k$ so that the participant reaches a zero speed when the elastic band stretches for another $\dfrac{y}{2}$ (or just before the participand touches the ground).

In this case, the participant would be brought back exactly on the top of the building (of course, if we neglect any force of resistance to the motion).

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