anonymous
  • anonymous
A particles position as a function of time is given by u = cos 2t i+sin 2t j ( The u, i and j should have tilde's underneath as they are vectors) (a) find the equation of the path
Mathematics
katieb
  • katieb
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amistre64
  • amistre64
x = cos(2t) y = sin(2t) z = 0
anonymous
  • anonymous
thats not the answer i sorta know how to do it but the 2t throws me off abit
amistre64
  • amistre64
thats the equation of a line in R^3 :) well, except for an initial point

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amistre64
  • amistre64
the position path just produces a unit circle
anonymous
  • anonymous
yes i understand that but normally you would eliminiate the sin and cos by squaring x and y then adding them
anonymous
  • anonymous
im not sure what happens to the 2t
amistre64
  • amistre64
2t just modifies the speed of rotation; nothing more
amistre64
  • amistre64
its going twice as fast around the unit circle
anonymous
  • anonymous
i see so the working is like this; x = cos 2t y=sin2t x^2=cos^2t y^2=sin^2t x^2+y^2=1 i ignore the 2t correct
amistre64
  • amistre64
or simply redefine it; 2t = u
amistre64
  • amistre64
it has no importance on position; other than it a given t it is at this location; but the path remains unchaged by it
amistre64
  • amistre64
tell me; does a person walking along the sidewalk get to the same place as the person jogging on the sidewalk?
anonymous
  • anonymous
yes thats correct. thanks so much you actually made me understand the question.
amistre64
  • amistre64
youre welcome :)

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