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**1. Homework Statement**

A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30° to the original path, determine

- the speed of the first ball after the collision.
- the speed and direction of the second ball after the collision.

**2. Homework Equations**

m1v1 + m2v2 = m1v1' + m2v2'

1/2m1(v1)^2 + 1/2 m2(v2)^2 = 1/2m1(v1')^2 + 1/2m2(v2')^2

**3. The Attempt at a Solution**

Ok. I have 3 unknowns in this equation. The v1', v2' and the angle of the second ball. For this I need 3 equations

For the X component I have:

V1 = v1' * Cos 30 + v2' * Cos θ

For the Y component I have:

v1' * Sin 30 = -v2' * Sin θ

Using the Conservation of energy I have:

V1^2 = v1'^2 + v2'^2

From here, I'm not sure where to proceed. I have tried some substitutions but I get into really long ugly math that turns circular and I never get anywhere. Any help would be appreciated. I know I need to use the trig relation of

Cos^2 θ + Sin^2 θ = 1, but i've not been able to get to any point where I can apply it.

Thanks in advance for your help.