infx, The problem does not state that the plane matches the speed of the belt, it says that the belt matches the speed of the plane.

"Relativity" has fuck-all to do with it. No E=mc'2 here.

The casual observer not on the conveyor would watch the plane take off as any other plane on a normal runway would.

The conveyor cannot keep the plane in place because it exerts force only on its wheels, which rotate to negate friction.

A plane with its gear locked up, if it powered up, would move forward on a fixed surface. It would not be smooth, but it would move. Trust me. Now is that more or less friction than the conveyor acting on free spinning wheels?