Richard P. answered • 02/25/18

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Richard P.

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Let p

_{0}be the initial momentum, p_{1}be the final momentum of the first ball and p_{2}be the final momentum of the second ball.._{ }These are vector quantities. The conservation of momentum can be written as p_{0}= p_{1}+ p_{2}. This is a vector equation. However, it can be made into a scalar equation by squaring both sides. The result is p

_{0}^{2}= p_{1}^{2}+ p_{2}^{2}+ 2 p_{1}• p_{2}, where p_{1}• p_{2}is the scalar dot product of p_{1}and p_{2 . }Kinetic energy can be expressed as p

^{2}/2m. The conservation of kinetic energy can be written asp

_{0}^{2}/ 2m = p_{1}^{2}/2m + p_{2}^{2}/2m.The two conservation equations cannot both hold unless p

_{1}• p_{2}=0. This condition means that the vectors p_{1}and p_{2}are perpendicular. This is the same as saying that the angle between them is 90 degrees.
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02/26/18

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02/25/18