Elastic Collision and final speed

[learnin']

Homework Statement

a) Initially, mass one (2.40 kg) has a velocity of 5.70 m/s and mass two (2.20 kg) is at rest. After they collide, mass one emerges at an angle theta = 31.0 degrees. What is the speed of mass one after the collision if the collision is completely elastic? (Note, there are actually two possible answers two this problem, choose the solution which has m1 going as fast as possible.)

b) What is the angle phi, between mass two's velocity and the initial velocity of mass one? (Give your answer as a positive number in degrees.)

c)What is the final speed of mass two after the collision?

m1= 2.40kg
v1i= 5.70m/s
m2 = 2.2kg
theta1= 30 deg
v1f= ??
theta 2 = ??
v2f = ??

Homework Equations

Because it's elastic,

mechanical energy is conserved.
1/2 m1(v1i)^2 = 1/2m1(v1f)^2 + 1/2m2(v2f)^2

Momentum is conserved
for x direction: m1v1i= m1v1f cos(theta1) + m2v2f(theta2)
for y direction: m1v1i= m1v1f sin(theta1) + m2v2f(theta2) = 0

tan (theta2) = (v1f* sin (theta1))/(v1i - v1f * cos (theta1))

The Attempt at a Solution

In all honesty, I'm a little thrown off because I don't know what v1f is.

 

[learnin']

I tried dividing the xdirection equation with ydirection equation and then getting 1 = tan (theta1) + tan(theta2)...but it didn't work... I need help... or a little guidance.