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**Billiard Balls--Elastic Collision**

I'm going through my old homework problems to prepare for the AP exam, and I got this right back in December, but now I have no idea how to solve it

## Homework Statement

A cue ball traveling at 7.0 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30° with its original direction of travel. Find:

a) the angle between the velocity vectors of the two balls after the collision

b) the speed of each ball after the collision

## Homework Equations

KE = 1/2mv

^{2}

p = mv

## The Attempt at a Solution

The collision is elastic, so both kinetic energy and momentum are conserved, so

1/2mv

_{0}

^{2}= 1/2mv

_{1}

^{2}+ 1/2 mv

_{2}

^{2}

v

_{0}

^{2}= v

_{1}

^{2}+ v

_{2}

^{2}

and

mv

_{0}= mv

_{1}+ mv

_{2}

v

_{0}= v

_{1}+ v

_{2}

The x component of the cue ball's final velocity is v

_{1}cos30

The x component of the target ball's final velocity is v

_{2}cosΘ

this gives me two equations, and three unknowns:

49 = (v

_{1}cos30)

^{2}+ (v

_{2}cosΘ)

^{2}

7 = v

_{1}cos30 + v

_{2}cosΘ

Am I missing something that will tell me the angle of the velocity of the second ball? Thanks