[fnord_too]

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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.

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I'm not talking about plausibility, I'm talking about possibility. If the engines are providing thrust, you cannot, as far as I can figure, have the plane not moving in relation to the conveyor belt frame (and thus the wind).

The thing about the wheels having angular velocity only is the real reason for this contradiction if I am thinking about this correctly. There is no way for the conveyor to counter the thrust of the engines so the plane will move forward. If the question said something like "the plane's wheels rest on a conveyor belt that turns with no friction" then the answer is clear, but Ray specificly says:

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The runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels

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I don't think there is a reasonable interpretation of that other than the wheels are not moving with respect to the conveyor frame (not considering the angular velocity) and thus the whole plan is stationary with respect to the air. I suppose the plane could be really long and the wheel axels free to move along the length of the plane, but that is quite a stretch.