Physic <span title="C..............!.............help">C..............!............</span> me..........plz!~?

Question

A block of mass m1 is at rest on a long frictionless table, one end of which terminates at a wall. A block of mass m2 is placed between the first block and the wall and set in motion to the left, toward m1, with constant speed v2i. Assuming that all collisions are elastic, find the value of m2 (in terms of m1) for which both blocks move with the same velocity after m2 has collided once with m1 and once with the wall. Assume the wall to have infinite mass.

Answer 1

After the collision, you will want m2 to rebound towards the wall with the same speed m1 goes forward.  m2 then hits the wall and they are both going the same speed in the same direction.

Momentum

m2*v2i = m1v1f -m2v1f

v2i = (m1 -m2)/m2 * v1f

v2i/v1f = (m1-m2)/m2

Energy

1/2m2*v2i^2 = 1/2m1v1f^2 + 1/2m2v1f^2

m2*v2i^2 = (m1 + m2)v1f^2

m2*(v2/v1f)^2 = m1 + m2

(v2/v1f)^2 = (m1+ m2)/m2

((m1-m2)/m2)^2 = (m1+ m2)/m2

(m1-m2)^2 = m1m2 + m2^2

m1^2-2m1m2+m2^2 = m1m2 +m2^2

m1^2 -3m1m2 =0

m2 =(m1)/3