A firework of mass 1 kg is placed on the ground and ignited , the impulse created by the explosion causes it to move vertically upwards with an initial velocity of 50 m/s,after 4 seconds a 2nd explosion takes place in air and the horizontal impulse forces cause it to separate into 4 identical pieces

***2 seconds after the 2nd explosion these 4 pieces travel horizontally in the same plane that the 2nd explosion took place and reach the vertices of a square of diagonal 80 meters 

Question : Find the horizontal velocity imparted on a piece after the 2nd explosion

So i tried applying the conservation of linear momentum , but i cant get an answer , can someone explain how i solve this type of problem ?

This is how I attempted the question :

P = m v   
P initial = P final   
1kg x 50 m/s = 1/4kg(V1 + V2 + V3+ V4)m/s   

I cant figure out the what to do next