A 0.400 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?
I know the equation for an elastic collision is (1/2)m1(v1)^2 + (1/2)m2(v2)^2 = (1/2)m1(v1')^2 + (1/2)m2(v2')^2 but I am not exactly sure how to plug the "The second ball moves off with half the original speed of the first ball." part into the equation. And for part B, I know KE is 1/2mv^2 but I have no idea where to begin to answer that question.. if anyone could help that would be great.
Start with the conservation of momentum.
m1V1=m1v1' + m2v2
where v2 is 1/2 V1
Then, solve that equation for V1' in terms of V1, m1, m2 *(you are given m1).
Now, write the conservation of energy..
1/2 m1V1 = 1/2 m1V1' + 1/2 m2V2 (remember v2= 1/2 V1), put for V1' what you got above, then turn the crank on the algebra to solve for m2)
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