Simple derivation for elastic collisions, where is my mistake?

[mathman44]

Homework Statement

http://postimage.org/image/j2ccrtjp1/

Here is a scan of my work. The problem is on the scan. Just trying to derive the velocity of the target in an elastic collision, as sketched in the image...

Can't seem to find the problem for the life of me.

 

[TSny]

Your work looks good and the expression you derived for u₂ is correct! You just didn't give the correct expression for what you claim the answer should be.

Usually people are more interested in writing the answer for u₂ in terms of the initial velocity v₁ rather than the final velocity u₁.