Conservation of mass with fireworks

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SUMMARY

The discussion centers on a physics problem involving the conservation of momentum in a fireworks explosion. A 3.0 kg rocket, moving at 4 km/h, explodes into three pieces of 1.0 kg each. Piece A travels horizontally at 4 km/h, while Piece B moves at a 37-degree angle downward at 5 km/h. To find the velocity and direction of Piece C, one must apply the principle of momentum conservation, setting up equations for both the X and Y axes to solve for the unknowns.

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Hi. This was the one extra problem credit problem I couldn't figure out in our momentum unit. (Since its not homework I posted here)

In a fireworks display, a 3.0 kg rocket moving at 4 km/h straight up explodes into three equal pieces of of 1.0 kg in mass. Piece A moves straight horizontally at a speed of 4 km/hr. Piece B moves at 37 degrees down from the horizontal and opposite piece A at a speed of 5 km/hr.

What is the magnitude and direction of the velocity of piece C?

My ideas: Well, since there's conservation of mass we know the velocity.

Can someone work this out for me?
 
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Can you assume that the momentum is preserved? If so then it's just:
[tex]M_TV_0 = m_1v_1 + m_2v_2 + m_3v_3[/tex]
Write that for two axes, X and Y, and separate the velocity vectors as well. You will have two equations with two unknowns. The unknowns would be the 3rd piece's velocity and the angle (direction) of that velocity.
 

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