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Conversion of Energy problem

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Hi, I have some confusion regarding the following question:
View attachment 210752 View attachment 210754
The answer is B but I'm confused as to why it is not D. The answer key cites the fact that since h is proportional to v^2, doubling h would cause v to increase by a factor of sqrt2. I would think that since h is doubled, v^2 would also be doubled which translates into a proportionality of 4v. Or would it actually be 4v^2 which still ultimately boils down to technically being...

Conversion of Energy problem

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