Found some more help so I\'ve made it mostly through this problem. Not sure how

Question

Found some more help so I've made it mostly through this problem. Not sure how to finish the last step.
2 shuffleboard disks of equal mass, one orange and the other yellow, are involved in a perfectly elastic glancing collision. The yellow disk is initially at rest and is struck by the orange disk moving initially to the right at 5 m/s. After the collision, the orange disk moves in a direction that makes anangle of 37 degrees with its initial direction, and the velocity of the yellow disk is perpendicular to that of the orange disk (after the collision). Determine the speed of each disk after the collision.
so far...
pi=pf
(initial) m1v1 + m2v2 = m1v1 + m2v2 (final) x component
(5m/s)v1 +m2(0) = m1cos theta + m2 cos phi
5m/s = v1 cos theta + v2 cos phi
then rearranged to
v2 cos phi = 5m/s - v1 cos 37 equation 1

for y
0 = v1sin theta + v2 sin phi
v2 sin phi = -v1 sin 37 equation 2

then divide 2 by 1

tan 53 = v1 .602 / 5m/s - v1 (.799)
1.33 = v1 .602/5 m/s - v1 .799

I don't know how to finish this? I know it should be simple, but having the 2 v1's is why I'm confused. Also equation2 was negative and when it was carried down (in the example) it wasn't. Thanks for the help!

Explanation / Answer

Separately, the x- and y-components of the total momentum are conserved. Pxi = m vorg,o + m vyel,o Pxi = m vo + 0 = m (5.0 m/s) + 0 Pxi = m vo Pyi = . . . = 0 We can substitute 5.0 m/s = vo at the end. Pfx = m vorg,x + m vyel,x Pfx = m vorg cos 37o + m vyel cos 53o Pfx = m vorg (0.8) + m vyel (0.6) Pfx = m [ vorg (0.8) + vyel (0.6) ] Pfx = m [ vorg (0.8) + vyel (0.6) ] = m vo = Pix vorg (0.8) + vyel (0.6) = vo Of course, this is one equation with two unknowns so we need some additional information. We will get that from looking at the y-equation for the conservation of momentum. Now, for the y-component, Pfy = m vorg,y + m vyel,y Pfy = m vorg sin 37o - m vyel sin 53o Pfy = m vorg (0.6) - m vyel (0.8) Pfy = m [ vorg (0.6) - vyel (0.6) ] Pfy = m [ vorg (0.6) - vyel (0.8) ] = 0 = Piy [ vorg (0.6) - vyel (0.8) ] = 0 Now we have two equations and two unknowns, vorg and vyel. 0.6 vorg = 0.8 vyel vorg = 1.333 vyel vorg (0.8) + vyel (0.6) = vo (0.8)(1.33 vyel ) + 0.6 vyel = vo 1.667 vyel = vo vyel = 0.6 vo vyel = 0.6 (5.0 m/s) = 3.0 m/s vorg = (1.333) (3.0 m/s) vyel = 4.0 m/s

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