[Phys-L] Re: projectiles

[frysingerj at COFC.EDU (James R. Frysinger)]

Anthony, my question would be, "Why is one needed?"

Perhaps its my perspective of continually teaching first year physics
students, but I find that I have to threaten instant Fs for the course
for anyone who uses a single range equation. Students come in from high
schools so attuned to one-equation solutions to all problems in life
that we do them a disservice, I feel, if we perpetuate that.

I tell them that during my career in the Navy I have shot many different
projectiles, from 45 caliber ammunition to torpedoes (armed only with
test instrumentation, thank God), and never was my aim point at the
same elevation as the launch point of that projectile. Thus, I never
give a problem with equal launch and landing point elevations. They
have to solve the vertical problem for time and then use that to solve
the horizontal problem.

Better to teach them multistep problem solving. This teaches them to
organize their thoughts and to design solution approaches.

Beyond that, one can teach them to do some simple programming on a
spreadsheet (i.e., entering of formulae) and then how to play "what if"
with the input parameters. This sets them up for modeling and for
playing with their data to determine the sensitivity of results to
uncertainties in the inputs.

Real life is too much fun to spend it looking for easy-solution
approaches.

Jim

On Thursday 2004 December 30 11:44, Anthony Lapinski wrote:
> Neglecting air resistance, we all know that the maximum range for a
> projectile occurs when the launch angle is 45° on level ground. But
what
> if the object is launched from a cliff of height H above the ground?
Here,
> the maximum range occurs at less than 45°. I've searched most of the
> college texts I have, but I can't find a "range formula" that has the
> height included. Is there such an equation with an initial height
(similar
> to R = v^2 sin2q/g on level ground)?