Solving Momentum Questions: Two Rolling Golf Balls Collision

[hulkster]

Ok. So I have spent about 40 mins on this question, and can't seem to get it. I know how to conserve momentum when an object hits another at rest, using the cosine and sine laws. but this question involves two objects both moving at different angles. We'll, here it is, if anyone can help:

Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2.70m/s[E] . After the collision, the velocities of the balls are 2.49m/s [62.8 degrees N of W] and 2.37m/s[69.2 degrees S of E]. What is the magnitude and direction of the unkown initial velocity?

The answer is 3m/s[W}...Any help would be greatly appreciated...Thanks.

 

[Hootenanny]

Have you drawn a diagram, show all the velocities?

 

[topsquark]

Ok. So I have spent about 40 mins on this question, and can't seem to get it. I know how to conserve momentum when an object hits another at rest, using the cosine and sine laws. but this question involves two objects both moving at different angles. We'll, here it is, if anyone can help:

Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2.70m/s[E] . After the collision, the velocities of the balls are 2.49m/s [62.8 degrees N of W] and 2.37m/s[69.2 degrees S of E]. What is the magnitude and direction of the unkown initial velocity?

The answer is 3m/s[W}...Any help would be greatly appreciated...Thanks.

Since momentum is a vector, if it is conserved, then it is conserved in all directions. So set up a coordinate system (E is +x and N is +y is fairly standard) and break everything up into components. So you have an initial momentum component for each golf ball in the x direction and the same for the y direction.
$$p_{01x}+p{02x}=p_{1x}+p_{2x}$$
and a similar equation in the y direction. Plugging in your known values (and taking vector components) leaves you two equations in two unknowns.

-Dan