Finding elastic band stretch to catch dropped egg from 2 meters

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Asubach
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Hi I am trying to find at what height i need to drop a egg from 2-6 meters. We will start with 2 meters. The weight of the egg and device holding the egg is .11kg together. I no the formulas for EPE and EP " EPE=1/2KX^2 AND PE=mgh. The question is now how to find where on the elastic band to hold from 2 meters above the ground without hitting the ground! "CLOSEST THE BETTER"

Thanks
 
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