The "Plane on a Treadmill" Question

[glatt]

Originally Posted by Flint

There are two interpretations for this. Both are possible, but neither is specified by the provided information.

#1: If the "forward speed" is defined as relative to the treadmill then the plane is stationary relative to the air.

#2: If the "forward speed" is defined as relative to the ground, then it is possible for the plane to be in motion relative to the air.

Nothing in the question rules out either of these interpretations, and no amount of blustery hoopla or physics masturbation can change that.

The question was written from the point of view of an observer, right? That observer is the one doing the measuring of the forward speed. It's forward speed relative to the observer.

That observer could be:
1. standing on the ground,
2. floating in the air,
3. standing on the treadmill, or
4. sitting in the plane

1&2: If the "forward speed" observer were in situation 1 or 2, the question would be written as it is, and the forward speed of the plane would be measured relative the the observer, which is the same as the ground. This would be your interpretation #2. It's how I and most here read the question.

3: If the observer is standing on the treadmill (3), he/she would have the perspective of the treadmill. If the treadmill starts moving, the observer won't feel motion because they are attached to the treadmill, They will feel a tailwind. Since the observer is writing the question, the question would be about planes taxiing in tailwinds, not about moving runways. The question doesn't mention winds anywhere, so the question is not from the point of view of the treadmill, and the plane's forward speed is not measured from that reference. Your interpretation #1 above is not a credible interpretation of the question as written, because nowhere does the question mention wind. Wind is not a part of the question, and the question does not mention wind. While this post may contain wind, there is none in the question.

4:Finally, if the observer is in the plane, he/she will see both the ground move and the runway move even faster. I don't think anyone believes this is written from the point of view of the plane, so I won't go into it further.

[tw]

Originally Posted by glatt

The question was written from the point of view of an observer, right? That observer is the one doing the measuring of the forward speed. It's forward speed relative to the observer.

That observer could be:
1. standing on the ground,
2. floating in the air,
3. standing on the treadmill, or
4. sitting in the plane

We simply do the answer as demonstrated in post 152 and then change the answer to that 'observers' reference.

We do same thing with electricity. Which is ground? Earth? Breaker box? Computer motherboard? Any one can be ground. We can define any point as the reference point. We select any reference point only to make the problem easier to solve. Same applies to this problem.

We have three possible 'grounds' - points of reference. Four if we complicate the problem by considering an observer. The observer is completely unnecessary to the question - airspeed - velocity between airplane and air.

Air is a perfect reference point because a clearly defined relationship exists between air and the plane.

When the plane's engines throttle up, ...

And we have a known relationship between air and the runway or treadmill. Break a problem into parts. We do all numbers relative to air AND therefore have a simple answer.

Obviously - and this is just too simple for all the speculation - obviously -As the engines throttle up, the plane does take off whether it is on a runway or on a treadmill. Obviously because what the treadmill does is completely irrelevant to (independent of) airplane and air. Obviously plane's airspeed only involves a relationship between air and airplane. Obviously observer’s location and what treadmill does are completely irrelevant. Obviously wheels make that treadmill movement completely separate of (independent - not connected to) airplane and air. Obviously location of observer is completely separate from (independent of) airplane and air.

It is quite scary that so many cannot grasp these obvious and simple relationships. Some of these replies are making me feel like a genius. That scares me.