747 on a treadmill conundrum..

[Angrboda]

"Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

The question is misleadingly worded. If the bit about the conveyor belt is read to imply that the conveyor belt is moving as fast as the wheels, then the aircraft is stationary and will not take off. If the plane is moving forward at all, the wheels will be turning faster than the conveyor belt. It's hard to come up with another sensible interpretation of that phrase other than that it will be moving at the same speed. However, it doesn't exactly say that, just that it's designed to do so. If the conveyor moves slower than the wheels so that the plane can move, then the thrust of the engines will propel the plane to take-off speed and it will take off. As stated, however, there's a contrary implication in the question that the plane isn't moving.