What is the initial velocity of the second ball in a 2-dimensional collision?

[pinkyjoshi65]

Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2.7m/s (E). After the collision, the velocities of the balls are 2.49m/s(62.8 N of W) and 2.37m/s (69.2 S of E). What is the initial velocity of the second ball?

So i know that the masses are the same, and the initial velociy of the 1st ball.
Hence by using the conservation of momentum formula, I get
v_2= (V_1+V_2)v1
(here, the capital V's r the final velocities and the small v's are the initial velocities)
So now if it was one dimension, it straight forward. But since this is 2-dimensional, its confusing.

I know we have to draw somthing like a vector diagram. So, i tried doing that.
I tried attaching the file but I can't seem to do it. So, i'll try to explain the my diagram in words!

So one ball is moving in the north west direction, the other in the south east. I drew a line frm the centre of the 1st ball going NW. Thats V_1. With that line as the hypotunese, i drew V_1x and V_1y. And the angle betwee V_1y and V_1 is 62.8 degrees. SO i used cos and sine to figure out V_1x and V_1y. I did the same thing for the 2nd ball..This is all i could do...Any help..

 

[qspeechc]

Define an x-axis, say the West-East line, then Nort-South is your y-axis. The resolve everything along those two axes, and work with conservation of momentum in those directions.

 

[pinkyjoshi65]

i still don't get it..ok..so i know the final velocities of both the golf balls. Hence i found the components of each final velocity.
V1x= Sin(62.5)V1, V1y= Cos(62.5)V1
V2x= Cos(69.2)V2, V2y= Sin(69.2)V2
And by using the conservation of momentum formula, i got v2= (V1=+V2)/v1

 

[pinkyjoshi65]

so now if i take the y components of each, i'll get
0=(V1y+V2y)/v1y
But v1y should be zero too yes..?..This is what i could do...