Conservation of relativistic momentum for identical particles

[theusername8]

If a particle of mass M is at rest in a lab when it decays into 3 identical particles of mass m with:
particle 1: having a velocity of 4c/5 in the -i direction vector
particle 2: having a velocity of 3c/5 in the -j direction vector
particle 3: having an unknown velocity in a direction defined by an unknown Θ

how would a find the direction and speed of particle #3 with respect to the lab, with respect to particle #2. And also the ration of M/m

I've tried computing the average direction and velocity of particles 1 and 2 then reversing the direction vector but i think I'm going about it the wrong way.

thanks in advance guys.

 

[Simon Bridge]

How would you do this if it were not relativistic?

 

[theusername8]

i was able to solve v for #3 to be .837c at 29.4 degrees

 

[Simon Bridge]

How did you do that?

 

[theusername8]

used equation gamma(mu)=p . For particle #3 got a velocit of m<-4/3c,-3/4c>. arctan (3/4 / 4/3 )=29.36
now I am trying to use u_y'= u_y/(gamma(1-(u_xv/c^2))) to find the relative y velocity between them but ended up with 1.017c

 

[Simon Bridge]

For particle #3 got a velocit of m<-4/3c,-3/4c>

... what is the magnitude of this velocity?
What direction should the velocity be pointing in for momentum to be conserved?
(You should also specify the reference frame.)

Sounds like you are just plugging numbers into equations.
What was your reasoning?