How Do You Calculate the Final Velocities in a 2D Coin Collision Problem?

[alphadog0309]

Homework Statement

Two coins, one at rest (c1), the other flicked towards the other (c2). Initial positions are marked, as are final positions and angles. Coordinate system's origin is placed at center of C1 with +x in direction of C2's motion.
knowns:
$$\mu$$ = .36
V₁ = 0
C1 final position- 10.25 cm @ 16 degrees
C2 final position- 5.6 cm @ 302 degrees (-58 degrees)
m1 = m2

UNKNOWNS-
V2
V1F
V2F

Homework Equations

(x):
m₂v₂ = m_1fv_1fcos(16) + m_2fv_2fcos(302)

(y)
0 = m_1fv_1fsin(16) + m_2fv_2fsin(302)

(cons. of KE)

1/2m₁v₁² + 1/2m₂v₂² = 1/2m_1fv_1f² + m_2fv_2f²

(acceleration? idk if this is necessary...)

a = $$\mu$$g
-- derived from $$\Sigma$$F = ma = $$\mu$$mg... not sure if there should be any other forces in this...

The Attempt at a Solution

i keep getting .36587v_f² = 2.0767v_f²

i have a feeling i need to find v2 right before collision using v² = v_o² + 2a(x-x_o)

 

[member 553083]

with a = \mug but i have no idea how to use that equation to solve for v2 after the collision (v2f)any help is appreciated :)