a mass of 1 kg is thrown with a velocity of 100 m/s. after 5 second it explode into 2 parts. one part of mass 400g move down with25m/s. find the velocity of other part after collision

Hi,

As the mass projected upwards so after five seconds its velocity will be 50 m/s upwards and its momentum will be 50 in upward direction.

As the mass explodes and masses are divided into 2 parts of 600 and 400 gms.
As one part is moving downwards other one will move upwards.

So applying principle of conservation of momentum :
50 = (.6)v-(.4)25 which gives v=100. I.e the other part (600gms) will move upwards with a velocity of 100 m/s.