Is Ignoring the Y-Component in Billiard Ball Collision Calculations Correct?

[aatari]

Could someone please have a look at my solution and tell me if it makes sense. Although I am able to get the initial velocity that the question asked for, however the fact that I did not incorporate the y-component which is 1.2sin30 degrees into the solution makes me doubtful. If I do need to use that into the solution, how would that fit in? Please help!

1. Homework Statement

A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up traveling at 1.6 m/s.

Homework Equations

Pi = Pf

The Attempt at a Solution

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[haruspex]

Could someone please have a look at my solution and tell me if it makes sense. Although I am able to get the initial velocity that the question asked for, however the fact that I did not incorporate the y-component which is 1.2sin30 degrees into the solution makes me doubtful. If I do need to use that into the solution, how would that fit in? Please help!

1. Homework Statement

A 0.50 kg cue ball makes a glancing blow to a stationary 0.50 kg billiard ball. After the collision the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0° from its original path. Calculate the original speed of the cue ball if the billiard ball ends up traveling at 1.6 m/s.

Homework Equations

Pi = Pf

The Attempt at a Solution

View attachment 213143
[/B]

In what direction do you think the second ball will go?