How Fast Does the Third Piece Move After the Bomb Explodes?

[mneox]

Homework Statement

a bomb explodes into three pieces of equal mass. two pieces move off at 120 m/s at right angles to each other. how fast is the third mass moving?

Homework Equations

p = mv
pi = pf

The Attempt at a Solution

I know how to do most of these questions, it's just that the wording of this particularly one stumps me. How do I know which direction the third mass travels in?

That's what confuses me about this question. Thanks for any clarity that can be offered!

 

[housemartin]

Hello,

well usually in those problems it is also said how the bomb was moving before explosion, as it is not said in your problem, I assume that maybe it was thrown vertically upward and explodes at its maximum height, so speed before explosion is v0=0. What you need to use here is conservation of linear momentum, that is momentum before explosion must be equal to momentum after explosion. Assuming that speed before explosion was zero, after explosion sum of three pieces momentums must add up to zero too. Just remember that momentum is vector quantity, and in this problem you can split it in two rectangular components, for simplicity you can put momentum of first piece along y axis, and second - along x axis. Cause all three masses are equal - from this point you should know where third momentum vector should be pointing, and find its magnitude using Pythagorean rule.