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anonymous

  • 5 years ago

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

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  1. amistre64
    • 5 years ago
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    x = cos(2t) y = sin(2t) z = 0

  2. anonymous
    • 5 years ago
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    thats not the answer i sorta know how to do it but the 2t throws me off abit

  3. amistre64
    • 5 years ago
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    thats the equation of a line in R^3 :) well, except for an initial point

  4. amistre64
    • 5 years ago
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    the position path just produces a unit circle

  5. anonymous
    • 5 years ago
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    yes i understand that but normally you would eliminiate the sin and cos by squaring x and y then adding them

  6. anonymous
    • 5 years ago
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    im not sure what happens to the 2t

  7. amistre64
    • 5 years ago
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    2t just modifies the speed of rotation; nothing more

  8. amistre64
    • 5 years ago
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    its going twice as fast around the unit circle

  9. anonymous
    • 5 years ago
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    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

  10. amistre64
    • 5 years ago
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    or simply redefine it; 2t = u

  11. amistre64
    • 5 years ago
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    it has no importance on position; other than it a given t it is at this location; but the path remains unchaged by it

  12. amistre64
    • 5 years ago
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    tell me; does a person walking along the sidewalk get to the same place as the person jogging on the sidewalk?

  13. anonymous
    • 5 years ago
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    yes thats correct. thanks so much you actually made me understand the question.

  14. amistre64
    • 5 years ago
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    youre welcome :)

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