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Originally Posted by KenP
You're stupid. It will take off.
All the conveyor will do is cause the wheels to spin wildly. Imagine a rocket on wheels on the same conveyor. That rocket is going to take off...with the wheels spinning off.
What the wheels and conveyor do is irrelavent as none of that provides any propulsion. The wheels lower friction and provide for braking.
Theoretically, the conveyor could be moving backwards at double the speed of the plane and it still wouldn't matter. That would only cause the wheels to spin even faster, but the plane will still be getting thrust, moving forward and generating lift.
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That's not true. Newton's law of motion states that the rocket or plane wants to stay still. As power is applied, as soon as it wants to start to roll, the conveyor moves, sending the motion back to a zero point.
That's where the conundrum lies with this version of the question. The plane can really never get up to any speed because it can't get past zero simply due to the limitations of the question IF you make certain assumptions OR it will take off IF you make other assumptions.
If the speed of the plane will always be instantaneously matched, the forward movement of the plane will never increase relative to it's surroundings.
If the plane starts to move at x MPH and instaneously the belt moves it -X MPH, the body of the plane remains still and actually does not move from a math standpoint.
But, assuming it's not a fictional question and the plane can move past this fictional "barrier of movement" then, as the plane increases it's speed, the plane is moving through the air and the belt is moving beneath and theoretically moving the wheels twice as fast.
That's why there were apparently different versions of the question. The one here was too vague and allowed for the No answer to be argued. The ones Bluehummer posted, that said speed relative to the wheels, changes the whole argument and allows the "body" of the plane to move without respect to the wheels.