Solving Firework Explosion Homework Problem

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The problem involves a firecracker that explodes into three equal mass pieces, with two pieces moving at 130 m/s at right angles. The conservation of momentum principle is crucial, as the initial momentum is zero at the highest point of the toss. To find the velocity of the third piece, the momentum in both the x and y directions must be balanced, leading to the conclusion that the third piece's velocity is not simply 130 m/s. The correct approach involves calculating the resultant velocity using vector components, resulting in a speed of approximately 183.3 m/s for the third piece. Understanding momentum conservation is essential for solving this type of physics problem.
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Homework Statement



A firecracker is tossed straight up into the air. It explodes into three pieces of equal mass just as it reaches the highest point. Two pieces move off at 130 m/s at right angles to each other. How fast is the third piece moving?

Homework Equations





The Attempt at a Solution



I'm not sure what to do with this problem, I thought the third piece would be the same as the other two at 130m/s but this is not the case. What is there to do?
 
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Conservation of momentum

Initially the momentum is zero(because it was at the highest point and wasn't moving)

but now you have three pieces, so the x and y components of the three pieces' momentums(I hate saying momenta)must cancel so that Pi=Pf
 
so does Pi = 260(mass) and Pf = mass(velocity) so the masses cancel and the velocity is 260?
 
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