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MathGroup Archive 2004

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Re: Related rates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45770] Re: [mg45759] Related rates
  • From: "Sseziwa Mukasa,,(978) 536-2359" <mukasa at jeol.com>
  • Date: Sat, 24 Jan 2004 00:36:21 -0500 (EST)
  • References: <200401230815.DAA27745@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Jan 23, 2004, at 3:15 AM, DIAMOND Mark R. wrote:

> 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.

Assuming you have defined theta and z then:

D[theta[z[t]],t]

> But
> what is the appropriate way to set up such a problem in Mathematica?

Define theta[z] and z[t], then take the derivative of theta[z[t]] with 
respect to t.

> 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.

If you already know D[z[t],t] then you can simply write D[theta[z],z] 
D[z[t],t] as well.

Regards,

Ssezi


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