The "Plane on a Treadmill" Question

[Happy Monkey]

Originally Posted by Phage0070

Plane moves forward, relative to the ground, at speed X.(wheels spin at X, unless you are suggesting chunks of them are departing the plane)
Treadmill moves backward, relative to the ground, at matching speed X.
Wheels spin at 2X

Yes...

- so the treadmill must be moving at 2X.

No.

Or, more accurately, the treadmill is moving at 2X, relative to the plane. It it still, however, only moving at X relative to the ground, matching the plane.

The treadmill matches the plane speed, both speeds relative to the ground. The plane moves at X, the treadmill moves at X in the other direction, and the wheels spin as if the plane were moving at 2X.

[HungLikeJesus]

Originally Posted by Happy Monkey

Yes...

No.

Or, more accurately, the treadmill is moving at 2X, relative to the plane. It it still, however, only moving at X relative to the ground, matching the plane.

The treadmill matches the plane speed, both speeds relative to the ground. The plane moves at X, the treadmill moves at X in the other direction, and the wheels spin as if the plane were moving at 2X.

But then it's a circular question. For those saying that the plane doesn't move, relative to the ground, X = 0 and 2X = 0, so the treadmill doesn't turn and the plane can't take off. But if the treadmill doesn't turn, the plane can move as normal and will take off as from a normal runway. Which proves that the plane will take off.