Find Orig. Speed 3.0kg Mass After Frictionless Explosion

[ScullyX51]

Homework Statement

A 3.0 kg mass sliding on a frictionless surface explodes into 3 1.0kg masses. After the explosion the velocities of the three masses are: (1) 9.0 m/s north, (2) 4.0 m/s 30 degrees south of west, and (3) 4.0 m/s south of east. What is the original spped of the 3.0 kg mass?

Homework Equations

Pi=Pf
P=mv

The Attempt at a Solution

Pi=Pf
3v= (1)9+ (1)4+(1)4
I know this is wrong. I am confused about what to use for the magnitude and direction of these velocities. would it be 4tan(3) for both of them?

 

[tiny-tim]

A 3.0 kg mass sliding on a frictionless surface explodes into 3 1.0kg masses. After the explosion the velocities of the three masses are: (1) 9.0 m/s north, (2) 4.0 m/s 30 degrees south of west, and (3) 4.0 m/s south of east. What is the original spped of the 3.0 kg mass?
…
Pi=Pf
3v= (1)9+ (1)4+(1)4
I know this is wrong. I am confused about what to use for the magnitude and direction of these velocities. would it be 4tan(3) for both of them?

Hi ScullyX51!

Momentum is a vector, so you must use vector addition, not ordinary addition.

(since there are four vectors, a vector triangle won't be very much use , so: ) use x and y coordinates.