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Re: buoyant bullets.



On Tue, 4 Nov 1997, Richard W. Tarara wrote:

I'm probably being very dense here, but why isn't the x and y motion totally
separable. That is

Fx = -kvx^n

Fy = -kvy^n

Rick,

With n not equal to 1, the force law you propose here has the unacceptable
property that its magnitude and direction in *physical space* depends on
*your* choice of coordinate system. Nature never cares about the
coordinate system. If you need a concrete example to convince yourself of
this, try looking at what happens when n = 2, k = 1, vx = 1, and vy = 0
(giving F = 1 in a direction opposite the velocity) then calculate the
*same* force in a coordinate system that is rotated by 30 degrees. You
will find that its magnitude is reduced by 21% and that it's direction is
rotated by 12 degrees. Worse yet, it is no longer even opposite the
velocity!

Isn't it only the horizontal motion through the media that adds a horizontal
retarding force and the vertical motion that adds a vertical retarding
force?

Again, not in general; *only* for n = 1.

This is how I set up my calculation..with the x and y forces,
accelerations, velocities, and displacements calculated separately--good old
introductory, algebra-based physics.

That's probably why you got the funny results. And it's not a question of
algebra versus calculus-based physics. It's a simple matter of what is
right and what isn't.

Even with your formulae, since vy << vx, there should be little difference
in the results.

Depends on what you mean by "little difference." With your formula there
is *no* difference and with the correct formula there *is.* That's a big
difference!

John
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