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May 10th, 2017, 01:39 AM   #1
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Parametric equation

A metal bar has one end fixed at the origin, and rotates anti-clockwise at a constant
rate of ω radians per second; at time t = 0 it points along the x-axis. A beetle, starting
at the origin, walks along the bar at a constant speed of v metres per second.
What is its position at time t?

I know that the position of the end of the bar at time t is (Rcos(wt), Rsin(wt)).

But how do I get the position of the beetle? Thanks!

Last edited by skipjack; May 10th, 2017 at 03:37 AM.
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May 10th, 2017, 03:38 AM   #2
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At time t, how far along the bar has the beetle gone?
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May 10th, 2017, 03:41 AM   #3
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Beetle's distance from the origin is $r(t) = vt$ ...

$x= vt \cdot \cos(\omega t)$

$y = vt \cdot \sin(\omega t)$

Beetle's path of travel for a single rotation of the bar will resemble the attached graph ...
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File Type: jpg IMG_1564.jpg (67.5 KB, 0 views)
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