I think the reason why a lot of people get confused with this is because they try to envision an airplane working the same way as a car.
If you put a toy car going 10 mph forward on a treadmill going 10 mph backward, the car wouldn’t move. The same is true for a real car and a larger treadmill.
But why? Cars accelerate differently than airplanes do. They burn gasoline to provide energy to push a piston which moves the tires. The tires come into contact with the road and physically grip it to push the car forward. It’s the friction with the surface of the ground and tires that allows the car to both move and turn.
How is this different from an airplane? Because airplanes don’t move with their wheels, they move with their jets! The two large jets at the side of the plane provide thrust to push the thing forward through the air, the wheel is just there for a smooth takeoff and to support the weight of the plane, it doesn’t do anything to actually move the plane forward.
Still confused? Here’s another way to think about it. Pretend you were in a river where the water was pushing you back, but you wanted to go forward. If you simply swam forwards at 5 miles per hour, and the river pushed against you at 5 miles per hour, you’d get nowhere (car on a treadmill). Now imagine you were back in the river but this time there was a rope attached to your waist which was anchored to a stable horse outside of the river. Every time the horse moved forward (which is easy because it’s on land), it pulls you forward too because you are tied to it. You see how the force that the river exerts against you is irrelevant and you still move forwards? It’s because it is the horse that is doing the pulling, and the river can’t act on it.
Now in truth airplanes aren’t pulled by an external force, they push themselves with fuel. They are their own horse and their own rope, and the ground cannot act on them because their big turbines are in the air.
So how would you go about stopping an airplane from flying? If you were to get a large enough fan and turn it on in the direction that the airplane is trying to take off in, *that* would be enough to stop it. Now the airplane is pushing on the air to go forward, but you are also pushing on the air with your big fan to make it go backwards.
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