Finding Final Velocities in a Two-Dimensional Collision

[wesDOT]

Homework Statement

A 5.0-gram particle moving 60 m/s collides with a 2.0-gram particle initially at rest. After the collision each of the particles has a velocity that is directed 30° from the original direction of motion of the 5.0-gram particle. What is the speed of the 2.0-gram particle after the collision?

Homework Equations

conservation of kinetic energy equation
conservation of linear momentum equation and the x and y components

m1v1i=m1v1fcos(theta) + m2v2fcos(phi)

The Attempt at a Solution

m1=5
m2=2
m2=.4m1

theta=30
phi=30

Since the the only two variables I am missing are the two final velocities, I have tried solving one of the equations for mass2s final velocity and then subsituting that value into either the original equation or another one. Everytime i end with an answer that is not one of my choice. I am confused as to how i should go about find the final velocities.

 

[Doc Al]

conservation of linear momentum equation and the x and y components

m1v1i=m1v1fcos(theta) + m2v2fcos(phi)

That's good for the x-components. What about the y-components? (That will give you the second equation needed.)

 

[wesDOT]

That's good for the x-components. What about the y-components? (That will give you the second equation needed.)

0=m1v1fsin(theta)-m2v2fsin(phi) right?

 

[Doc Al]

0=m1v1fsin(theta)-m2v2fsin(phi) right?

Right!

 

[wesDOT]

Thanks a lot. That has been taunting me all day. I tried everything else but that. Yet that was so simple. Again, thank you.