Elastic Collision, Equal Masses

[Cruncher]

Okay, i have a problem here with 2 dimensional elastic collision between 2 balls with equal mass, they are both moving in different directions before collision

what i know:

v_x and v_y of both balls,
the slope of their movement, which can be converted to an angle with tan^-1 x

the problem is all I've got so far is momentum conservation with

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

but of course we have 2 unknown variables here v₁' and v₂'

so how do i use slope or angle to get v1 or v2 and then the other is easy to solve for.

thanks

EDIT: could i use impulse (J = Ft) and use a really small number of time and we know that J = p₂ - p₁

EDIT2: and where could i get the F in impulse from? can't really use Newtons second law of F = ma here because then i would need to know the acceleration of what it hit was which is essentially what finding J does for me... so anyone know of a better method??

cruncher

 

[A.T.]

Hints:

- treat it as a 1 dimesional problem along the collision axis (connects centers of the balls). nothing changes perpedicular to it

- m1 = m2 in your case

- use the reference frame of one ball for calculation (one initial v becomes zero)

- use google

 

[Cruncher]

i have searched google, i can't get much that helps me or i don't understand what it means, if i make it a 1d problem along the collision axis, i guess i need to find how much momentum in that direction, using triangles i assume with x and y momentum, but what if both circles are moving the same direction and slightly different angles, and different speeds (obviously cause if they were same speed and direction they wouldn't collide) so it comes and hits it from behind, there is no momentum acting against the other ball,