How to Correctly Calculate Velocity in a Two-Dimensional Elastic Collision?

[PiRsq]

I have a problem with this question,

1. Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2 m/s [E] After the collision, the velocities of the balls are 2.49 m/s [62.8° North of West] and 2.37 m/s [69.2° South Of East]. What are the magnitude and direction of the unknown velocity?

Basicall I did:

For x component:


V1 + V2 = V1'cos(180°-62.8°) + V2'cos(360°-69.2°)

I solved for V2

I did the same for the y component then I took the x and y component values and did the pythagoras theorem to get the angle and value...The value at the back of the book is 3 m/s and moving W for the initial velocity of the other ball...My answer was 4.7 m/s [20° South of West]

Whats my mistake?

 

[NateTG]

You certainly have the right idea. If you show more work I might be able to tell you where the problem is.

 

[PiRsq]

I've got two answers and one of them is at the back of book. How do I know which ball moves where?

 

[HallsofIvy]

Are you assuming conservation of energy (perfectly elastic collision)? If so you can use V1²+ V2²= V1'²+ V2'².

 

[NateTG]

Originally posted by HallsofIvy
Are you assuming conservation of energy (perfectly elastic collision)? If so you can use V1²+ V2²= V1'²+ V2'².

It's not necessary here.
He's got two unknowns, and two equations from conservation of momentum. The only unknowns are the x and y components of one ball's inital velocity, and the other inital and both of the final velocities are given.

 

[PiRsq]

Im assuming its a perfectly elastic collision since its two golf balls