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The whole problem boils down to, does this conveyor belt keep the plane stationary with respect to the air?

The simple answer to this is NO

Simple to you, perhaps. I didn't immediately get to this answer when I first thought about it. At first, I went down the path thinking that if the belt matched the speed of the wheels then the plane wouldn't move. It wasn't until Peter's post about fricition that made me realize the belt wouldn't be able to keep the plane from moving.

So you're right- but if it took a few of us longer to realize what was obvious to you from the beginning, give us a break!