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 with a diagonal of 80 meters.

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

I tried applying the law of conservation of linear momentum, but i can't get an answer. Can someone explain how I can solve this type of problem?

This is what I attempted:

$$P = m v\\ P_{initial}= P_{final}\\ 1\;\mathrm{kg} \times 50\;\mathrm{ m/s} = 1/4\;\mathrm{kg}\times (V_1 + V_2 + V_3+ V_4)$$

I can't figure out what to do next.

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 with a diagonal of 80 meters.

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

I tried applying the law of conservation of linear momentum, but I can't get an answer. Can someone explain how I can solve this type of problem?

This is what I attempted:

$$P = m v\\ P_{initial}= P_{final}\\ 1\;\mathrm{kg} \times 50\;\mathrm{ m/s} = 1/4\;\mathrm{kg}\times (V_1 + V_2 + V_3+ V_4)$$

I can't figure out what to do next.

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

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 with a diagonal of 80 meters.

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

I tried applying the law of conservation of linear momentum, but i can't get an answer. Can someone explain how I can solve this type of problem?

This is what I attempted:

$$P = m v\\ P_{initial}= P_{final}\\ 1\;\mathrm{kg} \times 50\;\mathrm{ m/s} = 1/4\;\mathrm{kg}\times (V_1 + V_2 + V_3+ V_4)$$

I can't figure out what to do next.