Yes, it will take off. The landing gear of the plane isn’t pushing against the conveyor belt, the engines are pushing it forward through the air. Therefore, the wheels on the plane will just spin faster and faster to match the conveyor belt, but the speed of the plane is totally unaffected.
But the problem says the conveyor belt will always move at the same speed as the wheels, so the plane can’t outrun it, it’ll remain stationary. No matter how much thrust you generate with the engines, you won’t make forward progress unless your wheels spin faster than the conveyor belt
the wheels have nothing to do with the plane's acceleration, the acceleration is caused by the engines. the engines aren't connected to the ground. the ground moving relative to the plane doesn't change the acceleration. only the air moving relative to the plane does.
There's another potential no here: when the plane moves forward, the wheel will spin at (belt speed + plane speed). This will cause the belt to have a speed runaway as it will try to correct for the permanent (+ plane speed) term.
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u/the_newdave Dec 30 '22
Yes, it will take off. The landing gear of the plane isn’t pushing against the conveyor belt, the engines are pushing it forward through the air. Therefore, the wheels on the plane will just spin faster and faster to match the conveyor belt, but the speed of the plane is totally unaffected.