Billiard Ball theorem

• Apr 24th 2008, 02:19 PM
njr008
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.
• Apr 24th 2008, 02:28 PM
CaptainBlack
Quote:

Originally Posted by njr008
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