(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A ball that is circling with x=cos(2t), y=sin(2t) flies off on a tangent at t=Pi/8. find its departure point and its position vector at a later time t (linear motion; compute its constant velocity v).

2. Relevant equations

v=dR/dt T=v/|v|= (dR/dt)/(ds/dt)=dR/ds.

3. The attempt at a solution

I have got to be the dumbest person on the planet. all I can think to do is this: R= cos(2t) + sin(2t). I thought after that it'd be a good idea to differentiate to find the velocity, but I'm not sure I'm doing it correctly. what I find is this: v=-2sin(2t)+2cos(2t). then I went to find |v|, but I'm don't know how to compute it when I've still got the t in there.

whatever I do there, it's just not coming out right with the answer key. (thank goodness I have at least one odd-numbered problem tonight!!) what the author says is this:

leaves at (sqrt(2)/2, sqrt(2)/2); v=(sqrt(2), sqrt(2)); R= (sqrt(2)/2, sqrt(2)/2) + v(t-Pi/8) which is the position at time t.

helppppp! I promise this is my last post tonight! =)

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# Homework Help: Tangent of a circle question

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