Consider a particle that moves in a plane according to the function r(t) = (sin t2, cost²) with an intial position (0,1) at t=0. What is the length of the path required for this particle to return to its intial position? If you were watching a race between two runners, one moving according to x=sin t² and y=cost² and the other according to x=sin(t) and y=cos(t), who would win and when would one runner pass the other runner?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider a particle that moves in a plane according to the function r(t) = (sin t2, cost2)
with an intial position (0,1) at t=0.
What is the length of the path required for this particle to return to its intial position?
If you were watching a race between two runners, one moving according to x=sin t²
and y=cost² and the other according to x=sin(t) and y=cos(t), who would win and when
would one runner pass the other runner?
Transcribed Image Text:Consider a particle that moves in a plane according to the function r(t) = (sin t2, cost2) with an intial position (0,1) at t=0. What is the length of the path required for this particle to return to its intial position? If you were watching a race between two runners, one moving according to x=sin t² and y=cost² and the other according to x=sin(t) and y=cos(t), who would win and when would one runner pass the other runner?
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