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Leigh Palmer wrote about a week ago (sorry I can't keep up with you folks)
in connection with a golfball range problem:
The ironic thing about the problem I quoted is that the person
who made it up felt it necessary to specify the value of g. If
the student is guided by that he will solve the problem somewhat
inelegantly, but I can't make my students (who must already have
done such problems in high school) see that there is merit and
beauty in the elegant solution.
This led me to ask the following questions:
(i) In this message does "elegant" mean "algebraic" and "inelegant" mean
"numerical?" Surely the amount of work required to solve this problem is
not less for the algebraic method. In fact, one could argue (and this is
just what many of my students do) that it is the numerical method which is
less work because you only have to carry a simple value from step to step
in your solution, rather than an often cumbersome algebraic expression.
(ii) But maybe I missed something. Is there a more elegant *method* of
solution to the golfer problem than plowing through the component equations
of kinematics (which requires using the quadratic equation and picking the
correct root BTW)?
To boil the issue down: I think most of us tell our students to manipulate
the equations algebraically before substituting numbers even when the
resulting final equations will never be used again. Of what value is this
for non-physics majors? Pretend I'm one of your introductory students and
try to convince me.