Re: Solution to a problem!!

["Bob Sciamanda" <trebor@velocity.net>]

I think one practical, calculational lesson which the student should
learn from this problem is that it is sometimes advantageous to NOT solve
the general problem first (and then substitute values); although it is
instructive to show how general equations can be written by using, eg,
absolute value symbols as Dave did. Even then, in applying the general
equations,  different "branches" must often be separately treated. The
pitfalls are there no matter what approach you use - that's why it's a
good problem.

In any event the general "anti-cranking" lesson is that any mathematical
model must be carefully written and examined for its applicability to all
physical possibilities under consideration, before the crank is turned!

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor
-----Original Message-----
From: David Bowman <dbowman@tiger.georgetowncollege.edu>
To: phys-l <phys-l@atlantis.uwf.edu>
Cc: dbowman@tiger.georgetowncollege.edu
<dbowman@tiger.georgetowncollege.edu>
Date: Wednesday, October 28, 1998 12:51 PM
Subject: Re: Solution to a problem!!


> So far I haven't yet seen anyone comment on the general solution to this
> problem for arbitrary values of the problem's parameter's.  Therefore I
> thought I would make such comments.
>
> Let v_s == J's sprinting speed.
> Let v_r == J's rowing speed relative to the a frame for which the water
is
>           at rest.
> Let v_w == the water's speed of the river.
> Let   W == the width of the river.
> Let T_0 == W/v_s = a characteristic "time" for the problem.
> Let   r == v_w/v_r.
> Let   s == v_s/v_r.
> Let   u == sine of the heading angle upstream of straight across the
river.
> Let t_1 == time interval for J to row across the river.
> Let t_2 == time interval for J to sprint along the far shore of the
river
>           to the apparition.
> Let t_t == t_1 + t_2 = total time interval for J's trip starting from
the
>           moment of J's entry into the boat.
>
> Using these definitions we can get expressions for t_1 & t_2 as:
>
> t_1 = T_0*s/sqrt(1 - u^2) & t_2 = T_0*|r - u|/sqrt(1 - u^2).
> . . .
> David Bowman
> dbowman@georgetowncollege.edu