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MathGroup Archive 2004

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Related rates

  • To: mathgroup at
  • Subject: [mg45759] Related rates
  • From: "DIAMOND Mark R." <dot at>
  • Date: Fri, 23 Jan 2004 03:15:59 -0500 (EST)
  • Organization: The University of Western Australia
  • Sender: owner-wri-mathgroup at

I'm trying to solve a fairly complicated system of related rates problems
and would like to use Mathematica to expand my knowledge of some of the mathematics,
as well as actually solve parts of the problem. I couldn't find any examples
on the archive of solving related rates problems and would appreciate some
advice. My perspective is essentially that of someone who can do most of
the calculations by hand but I have no idea how to approach the problem with

Just to put a bit of meat into this but keeping it much simpler that the
problem I really want, consider an oBject (B) approaching a bullseye that
has one ring at a distance R from the centre (C) of the bulls-eye. Distance
from target at time t is z[t]. Angle theta is angle RBC. How can I calculate
d-theta/dt. Easy enough by hand, with dz/dt as the approach velocity, and
using the chain-rule to obtain d-theta/dt from d-theta/dz and dz/dt. But
what is the appropriate way to set up such a problem in Mathematica? Is the
chain-rule explicit in the set-up? Should I be using DSolve, and if so how?
Do I need to create a dummy function for the velocity, or can I specify the
relationships between theta and z, and between velocity and z and go from

I've chosen this particular problem deliberately because of the inverse
trigonometric functions that arise both here and in the actual problem I

Guidance of any kind by way of
(1) reference to a book;
(2) web site;
(3) example
would be greatly appreciated.

I noted one comment on the archive where the author seemed to be saying that
learning the mathematics was the difficult part, and students could easily
construct the Mathematica for related rates problems. I'm not a student ... and my
problem is the reverse!

Mark R. Diamond

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