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Once again, the OP states that the conveyor does in fact matter. It presents a state where the conveyor and the wheels are moving at the same speed in opposite directions. You can't state that as a condition and then say "Well once you add thrust you can ignore that condition". Unless the OP actually said that, but it didn't, so I don't see how you can blame all these guys who read that and assume that the airspeed must be 0.

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I simply assumed since we were talking about a plane thrust would be a given condition of take off.