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Redd:
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Not directed at wookie, but OP is too far away:
Looks like we're not the first to have trouble with this
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The link gives this statement of the problem:
"A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).
The question is:
Will the plane take off or not? Will it be able to run up and take off? "
Totally different problem and easy to see the answer is Yes. The wheels just spin at twice the normal rate.
The OP's version is different, tying the conveyer speed to the wheel speed - which we all assume to mean the speed of the wheel spin. The answer to the OP's version is clearly, HUH?. It's true that as far as effecting the plane's thrust, it doesn't matter what the conveyer and wheels are doing, AS LONG AS THEY'RE NOT DOING SOMETHING THAT'S IMPOSSIBLE.
If I walk against a moving conveyer I must walk faster than it's moving in order to go forward. If I increase the speed of my step and the conveyer instantly does likewise, my back foot will move backwards exactly as fast as I step forward and I make no progress. The OP is asking the impossible with his version unless you convolute his meaning to match the version quoted above.
Thanks to Redd for the Link.
PairTheBoard