Two particles of masses m1 and m2 in projectile motion have velocities v→1 and v→2 respectively at time t = 0. They collide at time t0. Their velocities become v→1' and  v→2' at time 2t0 while still moving in air. The value of (m1v1→' +m2v2→')−(m1v1→ +m2v2→) is

The momentum of the two-particle system, at t = 0 isP→i=m1v→1+m2v→2Collision between the two does not affect the total momentum of the system.A constant external force (m1+m2)g acts on the system. The impulse given by this force, in time t = 0 to t=2t0 is (m1+m2)g×2t0∴ |Change in momentum in this interval = |m1v→'1+m2v→'2−(m1v→1+m2v→2)| =2(m1+m2)gt0