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Math Help - Circle w/ point sliding back and forth

  1. #1
    Member realintegerz's Avatar
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    Circle w/ point sliding back and forth

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  2. #2
    MHF Contributor
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    So point C is sliding only along the line AB.
    The warning then will sound if point C is at 0.5 units to the right of point A.

    Let's call point C' the position of point C when it is 0.5 units to the right of A.
    And point D' the position of point D at that instant.

    If we can get the x-coordinate of C', then that is also the x-coordinate of D'. Then we can get the y-coordinate of D' by using the circle equation.

    Draw a radius to A.
    By Pythagorean theorem,
    4^2 = (3 -2)^2 +(AC)^2
    AC = sqrt(16 -1) = 3.87298

    So the coordinates of A are ((1 -3.87298),3) = (-2.87298,3)

    Then the position of C' is ((-2.87298 +0.5),3) = (-2.37298,3)
    Hence the x-coordinate of D' is -2.37298 also.

    In the circle,
    (x -1)^2 +(y -2)^2 = 16,
    (-2.37298 -1)^2 +(y -2)^2 = 16
    (y -2)^2 = 16 -(-3.37298)^2
    y -2 = sqrt(16 -11.37699)
    y = 2.15012 +2
    y = 4.15012

    Hence, D' is (-2.37298,4.15012)

    Therefore, whenever D is between, and including, points (-2,37298,4.15012) and (-2.87298,3) along the circumference of the circle, the alarm rings. ----answer.
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