Can a Plane on a Treadmill Take Off?

"Doug" wrote:

The whole problem is confusing because
"An airplane on a runway sits on a conveyer belt that moves in the
opposite direction at exactly the speed that the airplane is moving
forward."

Moving forward with respect to what? The conveyor belt? (you gt the
answer that it WONT take off), or the air? (you get the answer that it
WILL take off).

AMBIGUOUS!!!

Yes, the problem could have been made uninteresting by removing any
ambiguity. But as stated, it is very common (almost universal) to
speak of movement of a terrestrial object with respect to the surface
of the earth. If another frame of reference is intended, it is almost
always specified. Two movements are mentioned in the problem. Is
there any reason to suspect that one is movement relative to surface
of the earth (the conveyor) and the other is movement relative to the
first object? Why not th other way around, in which case the conveyor
is just an ordinary runway?

If you are not willing to resolve that ambiguity by assuming
conventional frames of reference, you might as well assume that one is
speaking of velocities relative to a solar system frame, in which case
the plane may be going very very fast forward, backward, sideways, up,
or down, depending on time of day and orientation relative to the
earth. The problem makes a lot more sense assuming conventional use
of "moving".
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