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Movement of Wedge - Newtons laws

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A.) A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest. Calculate: i) the acceleration of the wedge ii) the horizontal and vertical components of the acceleration of the block. (Do these answers reduce to the correct results when M is very large?) B.) The wedge and the block now have a horizontal force P applied to the wedge. What magnitude must P have if the block is to remain at a constant height above the tabletop?

I've posted this one before. I got an answer from one of the TA's which was good, but I'm still a little confused. So I thought I'd ask again if someone can provide me with another breakout of this one keeping it as simplified as possible. Thanks!

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Answer in a 4 page MS Word document with diagrams and explanations.

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Please see the attached Word document for the answer and diagrams

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If M is not moving the block of mass m will slide down to the wedge. If M is moving, the distance that the mass m covering will be less, and the actual trajectory is sketched as below, where aM is the acceleration of the block relative to the wedge of mass M.
The horizontal and vertical components of a are,
and ,

Now look at the free body diagram of the wedge and the block

For M: (1)

There is a contact force between the block and the wedge and between the wedge and the table. When the bodies are on a ...

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