Mapertius's Principle and 2nd Newton's law

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MP97
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Hi, I have been working on deriving the second Newton's law from the Mapertius principle applied to a perfectly elastic collision from a free fall acceleration problem. These are my calculations, but I keep getting a coefficient of 2 in my final answer for some reason. Could someone explain to me what I am doing wrong?

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I appreciate any help you can provide!
 

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