Simple isn't it? #6

Classical Mechanics Level 5

A group of friends from BRILLIANT decide to go for a bungee jumping camp. The first one to jump is Adarsh. He jumps from the top of a cliff of height $H$ . He performs a damped oscillatory motion along the vertical motion. The first time he reaches at the lowest level ,i.e, height of $0\text{ m}$ above the ground. Then he goes up to a certain height. Similar type of motion goes on until an equilibrium state is obtained at height $h=\frac{51H}{200}$ .

Find the original length length of rope used for bungee jumping.

The length is of the form $\frac{aH}{b}$ , where $a$ and $b$ are positive co-prime integers.

Find $a+b$

Details and Assumptions

Nothing bad happens to Adarsh.
Consider Adarsh to be a point sized particle.

This problem is of this set.

The answer is 17.

1 solution

Alex Wang
Jul 19, 2015

At the lowest level, Adarsh's velocity is 0. Using Conservation of Energy, $mgH = \frac{1}{2} k (H-L)^2$

At the final equilibrium state, the net force is 0. Therefore, $mg = k (\frac{149}{200}H - L).$

Substitute for mg from the second equation into the first, and k will cancel as well, giving us $L = \frac{7}{10} H$ or $\boxed{17}$ as our final answer.

Simple isn't it? #6

This problem is of this set.

The answer is 17.

1 solution

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