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## Homework Statement

Consider an elastic collision (ignoring friction and rotational motion).

A queue ball initially moving at 2.6 m/s strikes a stationary eight ball of the same size

and mass. After the collision, the queue ball’s final speed is 1.2 m/s.

Find the queue ball’s angle (theta) with respect to its original line of motion.

Answer in units of ◦.

I've attached a picture to make it a little clearer

## Homework Equations

kinetic energy = 1/2mv^2

momentum = mv

## The Attempt at a Solution

I've tried a couple of things, but its really the math that's tripping me up I think.

First I found the velocity of the ball that was hit. I got 3.504...etc. using the kinetic energy equation.

The next thing I did was try to solve it in terms of the two angles, theta and phi. Since the two y-components must be equal to zero (because there was no y component to the original velocity),

Eq. 1: 0 = 1.2 sin(theta) + 3.504 sin(phi)

And because the x components must add up to the original x velocity,

Eq. 2: 2.6 = 1.2 cos(theta) + 3.504 cos(phi)

When I try to make these into a system, I get a very unruly equation that leaves me dumbfounded.

My alternative was to separate each of the two velocity vectors into their components, and this ended up getting me a four equation system which again, left me dumbfounded.

By similar logic to above, the four equations I came up with were:

v

_{xcue}+ v

_{xother}= 2.6

v

_{y cue}+ v

_{y other}= 0

(v

_{x cue})

^{2}+ (v

_{y cue})

^{2}= 1.2

(v

_{x other})

^{2}+ (v

_{y other})

^{2}= 3.504

Note: Everytime I typed 3.504 I actually used the full calculator value.

So my question, I guess, is whether or not there is a simpler way to solve this, and if not, if anyone could give me a hand with the math, its confusing me big time.