Related rates

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

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

**Follow-Ups**:**Re: Related rates***From:*"Sseziwa Mukasa,,(978) 536-2359" <mukasa@jeol.com>

**Re: Related rates***From:*"Sseziwa Mukasa,,(978) 536-2359" <mukasa@jeol.com>