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Math Help - Travelling along...

  1. #1
    MHF Contributor
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    Travelling along...

    We have a circle radius=25 miles, with center at origin.
    Traveller A is on circle's circumference, at A(20,15).
    Traveller B is on x axis, at B(39,0).
    They leave at same time, A travelling along the circumference counter clockwise,
    B travelling in a straight line, such that A and B arrive at point P(u,v) on the
    circle's circumference at same time.

    QUESTION:
    if the speeds of A and B are given, what is "easiest" way to calculate u and v?
    Say the speeds are A = a mph, B = b mph.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Wilmer View Post
    We have a circle radius=25 miles, with center at origin.
    Traveller A is on circle's circumference, at A(20,15).
    Traveller B is on x axis, at B(39,0).
    They leave at same time, A travelling along the circumference counter clockwise,
    B travelling in a straight line, such that A and B arrive at point P(u,v) on the
    circle's circumference at same time.

    QUESTION:
    if the speeds of A and B are given, what is "easiest" way to calculate u and v?
    Say the speeds are A = a mph, B = b mph.
    Convert to polars and express the speeds as angular velocities.

    CB
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  3. #3
    MHF Contributor
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    Thanks CB. That's too easy!!

    I should have stated the HOW that I'm after.
    1: get length BP (make it m)
    2: get length arcAP : simple nuff: a/b(length BP)
    3: get length chordAP (make it n)
    4: calculate u,v using m and n

    Reason for doing it that way: that's the level person I'm helping is at.
    In this example, a nice point P to use (integer coordinates) would be P(7,24);
    by "nice point P", I mean a point to "show how it works"....
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