Solving Firework Explosion Homework Problem

[cstout]

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?

 

[blochwave]

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

 

[cstout]

so does Pi = 260(mass) and Pf = mass(velocity) so the masses cancel and the velocity is 260?