[man]

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why are the more than one posts?

if there is no wind with respect to the airplane, it will not take off. if there is no wind with respect to the runway, it will take off. lift cannot be generated without wind with respect to the plane. (wind in the negative direction of the plane's orientation.)

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As far as I can tell, the system is impossible. The question seems to state that the plane is not moving wrt to the runnway, but this is not possible given the setup since the jets/props provide thrust and there is no way for the runway to exert an opposite force via the free rolling wheels.

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yeah, but it's an ideal system, so plausibility isn't what we're concerned with. I think the question means to state that the plane does not move with respect to the air, though:
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The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels. There is no wind.

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this of course doesn't make any sense in a strict way of speaking, because the wheels have angular velocity, not retcilinear velocity, but you get the idea. the engines of the plane have nothing to do with the system, though. they exist only as a means of propulsion so that "wind" will be generated with respect to the plane.