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# Physics question.?

Two billiard balls of equal mass (m) collide elastically. Initially the 13 ball has speed (v) and the 9 ball is at rest. After the collision the 13 ball has speed (1/2v) and the 9 ball has speed Vf. What is Vf?

The professor says that Vf is (sqrt(3))v/2. Can someone help me with the steps it takes to reach this answer?

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if they collided head on then the 13 would be at 0 and 9 would be at v

owing to their equal masses

but that is not the given case so they must have glanced off of each other at a non-zero angle

with elastic collisions both momentum and kinetic energy are conserved

so

1/2 m V1^2 + 1/2 m V2^2 = 1/2 m V3^2 + 1/2 m V4^2

1/2's cancel as do all m's giving

V1^2 + V2^2 = V3^2 + V4^2

substituting given information we get

v^2 + 0 = (1/2v)^2 + vf^2 = 1/4 v^2 + vf^2

Vf^2 = 3/4 v^2

vf = sqrt(3/4 v^2) = sqrt(3)/2 v

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