Imagine there is a treadmil that is big enough to fit a plane and can match the planes speed. So if a plane traveled on it at 100mph it would travel backwards at 100mph.
If both the plane and treadmill could accelerate to no ends(basically travel at speed infinite) and the friction would never melt the wheels. Would the plane be able to fly?
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May not be correct but I believe if both had no limit to speed then yes the plane would take off eventually, however if somehow this was real and speed was limited to as it is today then the answer is no.
This is because eventually the air generated from the treadmill will be enough for the wheels to get off the ground. Since a plane is propelled from turbine engines and not your standard car engine, it does not rely on the wheels to move so when the wheels lift off the treadmill in the slightest bit it will jump forward enough to generate the wind needed to ascend into the sky.