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Old 03-05-2006, 10:28 AM
zut zut is offline
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Join Date: Apr 2000
Location: Detroit, MI
Posts: 3,724
Originally Posted by enipla
Where does the question state ‘Wheel Speed’?
bolding mine
Sorry, but you’re the one changing the question.
Already covered:
Originally Posted by zut
In any case, there are multiple interpretations of the problem, and the "answer" depends on your interpretation and your initial assumptions. flight lays out the two basic camps: The first is where the belt matches the plane speed with respect to the ground (that's what you're talking about). The second is where the belt matches the wheel rotation speed (or the belt matches the plane speed with respect to the belt). This requires the plane to remain stationary; otherwise the condition of the problem is violated. This second interpretation is (I think) what Paradoxic is talking about.

I've seen different wordings of the question (Cecil's original column had multiple versions, for example) that more or less strongly imply one interpretation or another. So I don't think it's necessarily conclusive to tie the "answer" to one wording or another, because other people have likely made conclusions based on alternate problem statements.
From the first column:
Originally Posted by Cecil
As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation."
You're assuming one version of the question. Nothing wrong with that. Paradoxic is assuming another. Nothing wrong with that either.

I suppose you could argue that your interpretation is more semantically correct for the given problem statement. However, note that in response to the same problem statement, Cecil himself explicitly states that "if the treadmill continues to accelerate" then "the plane stands still and doesn't take off." Admittedly a confusing flip-flop on his part, but it does illustrate the different interpretations of the question.