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Math Help - Billiard Ball theorem

  1. #1
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    Question Billiard Ball theorem

    I got this question in my vector calculus class and I am not really sure how to work it out.
    Two billiard balls of equal mass collide. If
    u = v + w, u^2 = v^2 + w^2,
    are equations representing momentum and energy conservation for the collision, prove the billiard ball theorem: namely that the vectors v and w subtend an angle of ninety degrees after the impact.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by njr008 View Post
    I got this question in my vector calculus class and I am not really sure how to work it out.
    Two billiard balls of equal mass collide. If
    u = v + w, u^2 = v^2 + w^2,
    are equations representing momentum and energy conservation for the collision, prove the billiard ball theorem: namely that the vectors v and w subtend an angle of ninety degrees after the impact.
    The first equation tells you that the vectors u, v and w form a triangle, and the second tells you that the sides satisfy Pythogoras' theorem, hence by the converse of Pythagoras' theorem the triangle is a right triangle (with the right angle between the sides v and w). Hence the vectors v and w subtend an angle of ninety degrees after the impact.

    RonL
    Last edited by CaptainBlack; April 25th 2008 at 05:50 AM.
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