Gillette
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An Jet aircraft is on a runway that is also a conveyor belt. The conveyor exactly matches the aircrafts movement BUT is going in the opposite direction of the aircraft. Will the aircraft be able to get airborne?
The problem as posed says nothing about the wheel. The treadmill moves in one direction at exactly the same speed that the airplane moves in the other direction (as I interpret the wording). There's no requirement that the airplane even be touching the runway/conveyor for the postulated conditions to be met.
DC_DEEP's summary of the physics is entirely sound. Airplanes fly by virtue of air speed, not ground speed.
The use of the word on rather than over denotes that they are in fact touching.
If you assume the two aren't even touching then doesn't that mean the plane is already airborne, making the entire question moot?
If the treadmill is moving backwards at speed V, the plane must be moving forwards at speed V. That was how the problem was stated. When the plane V equals the takeoff speed, up she goes. What the treadmill is doing in the meantime doesn't enter into it.
If you're only focusing on sentence structure the use of the word movement in place of thrust, speed, power or momentum does imply that the plane is in actuality "moving". That may mean that there is 400km/hr thrust of the engines vs 200km/hr speed of the conveyor but that would provide each with a directional speed of 200km/hr. So yeah, if you nit-pick the sentence structure this is the answer. She flys.