A bomb of mass 1 kg is thrown vertically upwards with a speed of 100m/s. After 5 seconds it explodes into two fragments. One fragment of mass 400 gm is found to go down with a speed of 25m/s. What will happen to the second fragment just after the explosion? $\left(g=10m/s^2\right)$

Speed of bomb after 5 seconds,

$v=u-gt=100-10\times 5=50m/s$

Momentum of 400g fragment

$=\frac{400}{1000}\times \left(-25\right)$ (downward)

Momentum of 600g fragment $=\frac{600}{1000}v$

Momentum of bomb just before explosion = $1\times 50=50$

From conservation of momentum

Total momentum just before collision = Total momentum just after collision

$\Rightarrow 50=-\frac{400}{1000}\times 25+\frac{600}{1000}v$

$\Rightarrow v=100m/s$  (upward)