[lgas]

[ QUOTE ]
Good. Anyone who can't understand after thinking about the rollerskates on treadmill example or the stroller on moving walkway example is just a fool.

[/ QUOTE ]

The problem is that those two examples don't take into consideration the one condition from the OP:

[ QUOTE ]
The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels.

[/ QUOTE ]

Neither the treadmill or the moving walkway would speed up/slow down to match the speed of the rollerskates/stroller.

Since much of the confusion in this thread seems to come from people's confusion as to whether the magical speed-matching conveyor belt from the OP somehow negates the ability of the plane to move forward, I don't think these examples with normal every day non-magical conveyor-belt-like devices are sufficient to make the solution clear to everyone.

Personally I think the problem comes from the magical conveyor-belt condition in that it couldn't possibly exist in real life. If somehow it did, I imagine what would happen is that the plane's forward velocity would exceed the rotational velocity of the wheels and the wheels would rip off... then the plane crash to the earth because it would not have acheived full take-off velocity yet... but the conveyor belt would've stopped moving at this point since the wheels would've stopped moving, so now the plane would go skidding off the magical conveyor belt on its belly onto the tarmac (or whatever surrounds the magical conveyor belt) and then the problem becomes reduced to whether the plane in question can take off with its landing gear up (or in this case, sheered off). I'm guessing most planes can't, but I don't really know for sure.

Edited for typos.