What Determines the Outcome in an Elastic Collision Between Two Croquet Balls?

[anightlikethis]

Homework Statement

A 0.180 kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball.(a) What is the mass of the second ball?(b) What fraction of the original kinetic energy (KE/KE) gets transferred to the second ball?

Homework Equations

a)1/2Mava^b+1/2Mbvb^2=1/2Mav2a^2+1/2Mbv2b^2

b)mava+mbvb=mav2a+mbv2b

The Attempt at a Solution

I solved for "v2a" using equation b and got mb2.77777va I then plugged this back into equation a and got (.5)(.18)(va)^2=(.5)(.18)((mb)(2.77777)(va))^2+(.5)(mb)((.5)(va))^2. If I've done this correctly I still don't know how to solve it correctly to find the mass of "ball b"

 

[Mentz114]

You can factorize m_b from the right-hand side of your final equation. I haven't checked if it's correct but your method obviously is.