Collision between snooker balls

[hmparticle9]

Homework Statement

Two identical frictionless balls are symmetrically hit by a third identical ball with velocity v_0i. Find all subsequent velocities.

Relevant Equations

Conservation of mass and conservation of momentum.

Two snooker balls are at rest and a third collides with the two of them. There is no friction and all balls are identical. The initial velocity of the ball (1) is $v = v_0 i$. I can understand the direction that the balls go in after the collision. But I want to know the resulting velocities of all the balls in play. The collision is elastic.

Here is my attempt

 

[haruspex]

Homework Statement: Two identical frictionless balls are symmetrically hit by a third identical ball with velocity v_0i. Find all subsequent velocities.
Relevant Equations: Conservation of mass and conservation of momentum.

Two snooker balls are at rest and a third collides with the two of them. There is no friction and all balls are identical. The initial velocity of the ball (1) is $v = v_0 i$. I can understand the direction that the balls go in after the collision. But I want to know the resulting velocities of all the balls in play. The collision is elastic.

Here is my attempt
View attachment 361361

Energy is not a vector. It only can be taken to be conserved overall, not separately per direction.

 

[JLT]

A fun simulation to try out is the PHET collision lab - you can define coefficient of restitution, give initial velocities, and set up collisions - choose the 2D model:

https://phet.colorado.edu/sims/html/collision-lab/latest/collision-lab_all.html

For your equations, energy is a scalar quantity, but momentum is a vector. Can you draw a picture of the x and y components for your mv's?

You should have
Σmvx = ...
Σmvy = ... (no initial vy, after collision one flies up and the other down)

Draw picture of velocities after the collision, break everything into Vx and Vy

 

[hmparticle9]

Got it! Thanks :D