Two particles of masses `m_(1)` and `m_(2)` in projectile motion have velocities `vec(v)_(1)` and `vec(v)_(2)` , respectively , at time `t = 0`. They collide at time `t_(0)`. Their velocities become `vec(v')_(1)` and `vec(v')_(2)` at time ` 2 t_(0)` while still moving in air. The value of `|(m_(1) vec(v')_(1) + m_(2) vec(v')_(2)) - (m_(1) vec(v)_(1) + m_(2) vec(v)_(2))|`

Explanation

As there is no external force in the horizontal direction their momentum is changed in the vertical direction only by the gravitation force in time 0 to `2 t_(0)`
As change in momentum = external force xx time interval
` :. (m_(1) vec(upsilon_(1) ) + m_(2)vec(upsilon_(2))) - (m_(1) vec(upsilon_(1))+ m_(2) vec(upsilon_(2)))`
` = (m_(1) + m_(2)) g x (2t_(0) - 0 )`
` = 2 (m_(1) + m_(2) ) g t_(0)` .