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

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In an elastic collision involving two croquet balls, the first ball, weighing 0.180 kg, collides with a second ball initially at rest, which then moves off at half the speed of the first. To determine the mass of the second ball, the conservation of momentum and kinetic energy equations are applied. The user attempted to solve for the final velocities and mass but encountered difficulties in isolating the mass of the second ball. They received guidance on factoring out the mass from their equations to simplify the solution process. The discussion emphasizes the importance of correctly applying conservation principles in elastic collisions.
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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"
 
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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.
 

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