How Do You Solve for Vf2 in a Momentum Equation?

[physicsfreak9]

I was assigned a problem where I had to derive a formula. We were given

m1Vi1 + m2Vi2=m1Vf1+ m2Vf2
and
1/2 m1Vi1 ^2 + 1/2m2Vi2 ^2= 1/2 m1Vf1 ^1 + 1/2 m2 Vf ^2

Somehow, using combination, I have to get a formula that says Vf2=
Both Vf2 and Vf1 are unknown. I thought I could set both equations = to Vf1, then set those equations equal, and do it out, but it isn't working. Can someone help? Thanks.

 

[hage567]

Can you post the problem? It would help. Also, if you could show what you tried in more detail we could maybe see where you're going wrong.

 

[physicsfreak9]

I'm afraid there was no more instruction, other than that. Let me see if I can say it better. Only Vf1 and Vf2 are unknowns, so we have to solve for them. System of equations is the way to do it, I was told. Another hint I got was that the final answer, which is Vf2=... does not have any m's, they all cancel out somehow. I hope that is clearer. Thanks.

 

[hage567]

So you weren't actually given a question to solve? Just those two equations together? That's a little strange to me. Well, just do like you said you did, arrange one equation for one unknown and put it into the other equation and solve for the second unknown. Unless you state the question or show your work I can't really do much else for you. If you want us to check your work for math errors post what you did.

 

[physicsfreak9]

Uh well if you set both equations equal to Vi1, the first one is

Vf1= (m1vi +m2Vi2-m2Vf2)/m1

and the second one is

Vf1= sqrt [(m1vi1^2 + m2Vi2^2-m2Vf2^2)/m1]

Then, you set them equal.

(m1vi +m2Vi2-m2Vf2)/m1 = sqrt [(m1vi1^2 + m2Vi2^2-m2Vf2^2)/m1]

This gets rid of the Vf1s, so now we need to solve for Vf2. Can you help me out on that?