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Determining the Maximum Separation

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The positions of two particles on the s-axis are s1=sin t and s2=sin(t+ π /3), with s1 and s2 in meters and t in seconds.
a) At what time(s) in the interval 0 ≤t ≤ 2π do the particles meet?
b) What is the farthest apart that the particles ever get?
c) When in the interval 0 ≤t ≤ 2π is the distance between the particles changing the fastest?

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Solution Summary

This solution helps with problems regarding maximum separation. It helps determine time when particles meet, the distance between particles, and intervals when particles are changing quickly.

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Please refer to the attachment.

a) At what time(s) in the interval 0 ≤t ≤ 2π do the particles meet?

Separation between the particles = s = s1 - s2 = sin t - sin (t + Π/3) .....(1)

For the particles to meet, the separation between them must be zero. Hence,

sin t - sin (t + Π/3) = 0 or sin t = sin (t + Π/3)

Or sin t = sin t cos Π/3 + cos t sin Π/3

Or sin t = sin t cos 60O + cos t sin 60O

Or sin t = 0.5sin t + 0.866 cos t

Or 0.5sin t ...

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