How to Solve an Elastic Collision of 3 Balls with Frictionless Motion?

[baubletop]

Homework Statement

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?

Homework Equations

m₁v_1i + m₂v_2i = m₁v_1fcos(θ) + m₂v_2fcos(θ)
KE = 1/2 mv₁² + 1/2 mv₂²

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!

 

[tiny-tim]

hi baubletop!

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

 

[baubletop]

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

 

[tiny-tim]

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

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

 

[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?

 

[tiny-tim]

(just got up :zzz:)

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

(forwards or backwards)

yup!

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

 

[vlad777]

I have exactly the same problem.
Can someone please explain and solve this? Please?

(baubletop have you ever solve this?)

Many thanks.