. For an elastic head-on (assumed) collision between equal masses, they simply swap velocities. The final velocities of objects 1 and 2 are 0 and v, respectively.
2. mv = (2m)u
where u = final velocity. Then u = v1 = v2 = v/2
3. Initially, p = (2m)v
final p = 2mv = 2mv1 + mv2
But for an elastic head-on collision, we know that the
relative velocity of approach = relative velocity of separation, or
v = v2 - v1
v2 = v + v1
plug into final p:
2mv = 2mv1 + m(v + v1) = 2mv1 + mv + mv1
mv = 3mv1
v1 = v/3
v2 = v + v/3 = 4v/3
4. initial p = mv
final p = mv = (m + 3m)u = 4mu
u = v1 = v2 = v/4
