No, it doesn't. We interpret the question differently. Your interpretation is not physically possible, and mine is.

No. It doesn't. All it says is that the treadmill moves backward as fast as the plane moves forward.

Hope this comes through. Never thought I'd see such excitement about a physics problem! :D

That's a nice drawing, but the belt force arrow is in the wrong spot. It applies force to the surface of the weel's tire, not the axle.

All the excitement, in this thread, is regarding a semantics problem.

Which doesn't matter, because the question states what the result is, not "how" it works.

And the stated result is that the plane moves forward.

What? Is this the line you're having problems with?

Because it absolutely does not mean "...as the plane moves forward, the plane moves backwards beneath the aircraft", if that is what you're thinking. Context, man, context.

The question does NOT ask if the belt can move fast enough to keep the plane stationary.

It just says that the belt moves backwards at the same speed as the plane moves forwards. I interpret speed as the movement of something relative to a stationary object, namely the ground.

So if the plane is MOVING (key word folks) forward at 100mph, the belt is moving backwards at 100 miles an hour. The wheels are spinning as if the plane where traveling at 200 miles per hour.

In this interpretation, the plane takes off.

OK. If I change the original question to:
"A plane is standing on a runway that can move, like a giant treadmill. When the engines throttle up, the plane begins to move forward, but the treadmill runs at the same speed as the forward speed of the plane, only in the opposite direction. So, as the plane moves forward, the treadmill moves backwards beneath the aircraft.

As the engines throttle up, does the plane take off?"

What would your answer be?

:::stops reading::: I'm discussing the original question.Interpretation #1: The plane “begins to move forward” relative to the treadmill, “but” because the treadmill, by whatever mechanism (not stated) moves the same speed, in the opposite direction, the net forward speed of the plane is zero.

Interpretation #2: The plane “begins to move forward” relative to the ground, and the treadmill “match[es] the forward speed of the plane” (relative to the ground) and moves this speed in the opposite direction, causing the wheels to spin faster.
Can you (or anyone) please elaborate on the reasons why interpretation #1 is not “physically possible” ???

The plane is not moving ith respect to the AIR, the only substance that matters in this question. No air movement over the wings, no lift, no takeoff. QED.

And it doesn’t have to. It states “the treadmill is made to match the forward speed of the plane, only in the opposite direction” so, based on whether you are considering the speed of the plane to be relative to the surface it is on, or relative to the surface next to the surface it is on, you get either #1 the exact speed needed to keep the plane stationary or #2 a speed completely irrelevant to whether or not the plane is stationary.

This is a wind-up thread based on an unstated distinction which produces two different results.

Because the speed of the plane is not determined by its wheels. If you had a treadmill set up according to interpretation one, and the plane was being towed by a truck that was not on the treadmill, as soon as the truck started pulling, no matter how fast the treadmill went, the plane would be pulled forward, because the wheels would just move at the towing speed plus the treadmill speed. And then the magic treadmill would speed up to match that, and the wheels would speed up to match that, etc, etc, and it would rocket up to infinity.

The wheels are unpowered, so they will always spin at the speed of the treadmill (re ground) plus the speed of the plane (re ground). If you then set the speed of the treadmill to match the speed of the wheel rotation, you get a recursive equation. They can't both rely on each other.

Is it the word "but" that confuses? Drop the word "but" in the original question and replace it with the word "and". The conjunction does not change the meaning of the question.