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Falling Rod on Smooth Floor (CM Coordinates)

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Please see attached. I know this problem sounds very strange and perhaps counter-intuitive, which is why I am asking it. I need to solve this problem a specific way, as given in the attached file, using the provided coordinates. Please do not attempt to solve this problem with anything other than the coordinates given.

I have also attached my last submission, which was apparently not acceptable. The response to this solution was: "Your method is not correct. You need to divide motion into KE of CM plus rotational KE about CM. The key is to find the position of the CM in terms of the independent degrees of freedom. Let X be the horizontal contact position of the rod. X_cm =X+L cos theta, Y_cm= L sin theta. The two degrees of freedom are X and theta. From these you can construct the KE. X is horizontal coordinate of the moving contact point. X is not fixed."

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The solution determines the CM coordinates of a falling rod on smooth floor.

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