# Homework Help: Elastic collision of 3 balls

1. Oct 31, 2013

### baubletop

1. The problem statement, all variables and given/known data
A ball with an initial speed of v1 = 21.5 m/s collides elastically with two identical balls whose centers are on a line perpendicular to the initial velocity and that are initially in contact with each other. The first ball is aimed directly at the contact point and all motion is frictionless.
>What is the speed of ball 1 after the collision?
>What is the speed of ball 2 after the collision?

2. Relevant equations
m1v1i + m2v2i = m1v1fcos(θ) + m2v2fcos(θ)
KE = 1/2 mv12 + 1/2 mv22

3. The attempt at a solution
So I know that the velocities have two components, x and y. I also know that at the collision point, the angle of the centers of mass are 30° (since the balls form an equilateral triangle).
For the x-component, I tried using the conservation of momentum equation above with cos(30°) and using the KE equation to substitute for unknown values of v1 and v2.
For the y-component I tried doing the same, but since the original velocity in the y-component is 0, I used
0 = m1v1sin(θ) + m2v2sin(30). For θ I tried 30, 60, and 180, but none of them worked.
Now I'm a bit stuck and I'm getting confused from all the variables I'm trying here. Any direction is appreciated!

2. Oct 31, 2013

### tiny-tim

hi baubletop!

what directions are you assuming for the three balls after the collision?

3. Oct 31, 2013

### baubletop

Should the first one go backwards since it's an elastic collision?

4. Oct 31, 2013

### tiny-tim

i'm not worried about backwards or forwards, just the line

(and now i'm off to bed :zzz:)

5. Oct 31, 2013

### baubletop

This is the diagram that came with the problem:

So the first ball would go forward, and the other two would move outwards 30° from that straight line, right?

6. Nov 1, 2013

### tiny-tim

(just got up :zzz:)
(forwards or backwards)

yup!

ok, now do components of momentum in the forwards direction, and energy

7. Apr 21, 2014