I have a drinking problem
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It flies. There are valid visualizations and formulaic proofs ALL OVER this thread. We've proved the system. We've proved the wording of the original question. We've proved the systematic interaction forces. And we've proved the existence of an EXTERNAL force from the jet's turbines.
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Stand on a skateboard holding a 100-lb weight. Throw the weight in one direction. You move in the other. THAT is the response of the air going through the turbines. EXTERNAL FORCE. Wheels irrelevant.
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A plane is standing on a movable runway(something like a conveyor) As the plane moves, the conveyor moves but in the opposite direction. The conveyor has a system that tracks the speed of the plane and matches it exactly in the opposite direction.
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look, the forces ar unbalanced...it'll move!