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Thread: Find a path that traces the circle....

  1. #1
    Jan 2008

    Find a path that traces the circle....

    im having trouble figuring out what the problem wants me to find.

    Find a path that traces the circle in the plane with radius and center with constant speed 8.

    thanks in advance!
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  2. #2
    Junior Member
    Nov 2008
    The best way to do this is to parameterize x, y and z. Since we're working in the plane y=-1, y is easy enough to parametrize, it's just y=-1. x and z are a little more difficult. Let's imagine for right now that the circle were centred at the origine, then x and z can be expressed as

    x=r\, cos(wt)
    z=r\, sin(wt)

    where r is the radius of the circle (r=2), t is the time and w is a constant we'll have to find for ourselves (it relates to the speed). Note also that the choice of cos for x and sin for z is arbitrary, we could have gone sin for x and cos for z.

    Now since the center has to be (3, -1, 2), just add 3 to x and 2 to z:

    x=2\, cos(wt)+3
    z=2\, sin(wt)+2

    From here all you have to do is find w and you're all done. Let me know if you need any more help on this.
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