@rob Re: Discussion of blue's Question "Is this the correct approach to find acceleration of the wedge?"

I see this question as being of the type "What is the error in my calculation?"

See blue's comment to Farcher's comment. Also blue's comment in the question, that the 1st equation might be incorrect.

Also the final question in the text : "Why is eqn 1 not applicable?" in this case.

I think the issue in blue's question is "Is eqn 1 correct? If not, what is my error?"

The accepted answer does not discuss any conceptual difficulty about applying conservation of energy to this scenario. It confirms that the equations correctly implement the conservation of energy and momentum, and points out the source of the error as a false assumption about the relation h(t) given in the problem.

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