A mass of $1kg$ is thrown up with velocity of $1000m/s$.After $5$ second , it explodes into two parts. One part of mass $400g$ moves soen with a velocity $25m/s$ calculate the velocity of other part just after the explosion $(g=10m{s}^{-2})$

The velocity of the mass after 5 seconds (just before the explosion) is

$v=u-gtv=100-10\left(5\right)v=50$

Since the momentum is conserved, the momentum before and after the collision is the same.

Take the direction upwards as positive. The conservation of momentum says,

$1\left(50\right)=0.4(-25)+(1-0.4)v\Rightarrow 50=-10+0.6v\Rightarrow v=100$

The velocity of the other part after the explosion is $100m/s$ upwards.