[Phys-L] Re: thrown ball with air drag

[ludwik kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

On Sep 14, 2005, at 3:17 PM, Carl Mungan wrote:

> Someone just came in and asked me a nifty problem. After diddling
> around a little we got the answer, but you all might enjoy it too:
>
> A ball is thrown vertically upward with initial speed v0. Assume air
> drag is proportional to speed squared. Let the speed of the ball just
> before it hits the ground be denoted v. Show that 1/v^2 = 1/v0^2 +
> 1/vT^2 where vT is the terminal speed of the ball.
>
> I feel like there must be some physical significance as to why this
> result comes out as a sum of inverse squares. (Doing the problem does
> not really shed any light on this interesting feature, at least the
> way I did it.) Anyone have any ideas about it?

Intuitively this result makes sense. If v0 is very large that v=vT,
like for a parachutes. And v=v0 when v0<<vT. Why are you looking for a
deeper physical significance?

Suppose you multiply each side by 2/m, where m is the mass of the ball.
This gives 1/E=1/E0 + 1/ET, where each E stands for kinetic energy.
Ludwik Kowalski
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