1-D Example Modified
We use the simpler second equation first:
m1v1i + m2v2i = m1v1f + m2v2f
to get v1f = (m1v1i - m2v2f)/m1 (since v2i = 0).
We use this value for v1f in the second equation:
(1/2)m1v1i2 + (1/2)m2v2i2 =
(1/2)m1v1f2 + (1/2)m2v2f2 + Elost
But we know Elost = 0 and v2i = 0, so we get:
(1/2)m1v1i2 + 0 = (1/2)m1[(m1v1i - m2v2f)/m1]2 + (1/2)m2v2f2 + 0.