Three particles break off after an explosion

[hime]

Homework Statement

An object with total mass mtotal = 20 kg is sitting at rest when it explodes into three pieces.
The first piece with mass m1 = 5 kg moves NW at an angle of θ1 = 20° above the –x axis with a speed of v1 = 30 m/s.
A second piece with mass m2 = 4 kg moves SE at an angle of θ2 = 25° to the right of the -y axis at a speed of v2 = 25 m/s.
The mass of the third piece is 11kg.
What is the x-component and y component of the velocities of the third piece?
What is the change in kinetic energies of the pieces after the collision.
Note that momentum is conserved and Pf=0.

Homework Equations

p=mv
pi=pf=0
KE=0.5*m*v^2
KE=0.5*p^2/m

The Attempt at a Solution

In x direction--> calculating the momentum
m1v1cos20=m2v2sin25+Px where Px is the momentum of the third particle in x direction
5*30*cos20=4*25*sin25+Px
Px=98.692

In x direction--> calculating the momentum
m1v1sin20=m2v2cos25+Py where Py is the momentum of the third particle in x direction
5*30*sin20=4*25*cos25+Px
Py=-39.32

 

[vela]

Did you use P_f=0?