Calculate Mass of Missing Piece Exploding Boulder

[yoleven]

Homework Statement

A stick of dynamite blows a boulder into 4 pieces. The boulder was stationary before the explosion. After the explosion, three of the pieces have the following momenta;
piece a = 10m/s West 1kg
piece b = 20m/s North 2kg
piece c = 10m/s East 4kg
Calculate the mass of the missing piece if the magnitude of its velocity is 25m/s

Homework Equations

Ptotal(initial)=Ptotal(final)
P=mv

The Attempt at a Solution

Since the boulder was not moving, its momentum is zero. The momentum of each piece is its mass x its velocity. Each piece's momentum added to each other will equal zero because momentum is conserved. So I get;
0=m1v1+m2v2+m3v3+m4v4
0=1kg(10m/s W)+2kg(20m/s N)+4kg(10m/s E)+m4(25m/s)
-90kgm/s=m4(25m/s)
m4=-3.6kg
Now I can't have a negative mass, so what can I do to solve this?

 

[P3X-018]

The momentum is a vector you can't just add all the components like that. It's a 2-dimensional situation.
And you have given the magnitude of it's velocity, ie it's speed. So you also to need to figure out in what direction the 4th piece goes, but you don't need to calculate it though, only that it will be in your equations.

 

[yoleven]

Thank you.