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Of course the plane has to be moving relative to the air around it (or the ground if that makes it easier).

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this is it, you need wind over the wings for lift!! a plane cannot get in the air without lift! wtf, i can't believe noone gets this

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Please explain specifically what FORCE is stopping the plane from moving forward (relative to the atmosphere, NOT the conveyor belt).

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Uh. The conveyor belt moves at the same speed as the
wheels as stated in the problem. Thus the plane cannot move forward.

Seriously how much physics do you understand? Are you familiar with reference frames?

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Explain how the wheels will move at the same speed as the plane in this example.

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THIS JUST IN:

WHEELS ARE ATTACHED TO THE PLANE

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dude, one sec. if the plane's velocity is 100 mph in the +x direction and the conveyor's velocity is 100 mph in the -x direction (and the turbines are off), we agree that the plane is not moving relative to the ground, correct?


now what happens if you apply a force to the plane in the +x direction? is it locked in space? can it not move?

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Yeah I totally agree with you here.

The thing is, as stated in the original problem, the runway speeds up to compensate for the extra +x force.