(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A kaon (denoted K0) is an unstable particle of mass 8.87 × 10−28kg. One of the means by which it decays is by spontaneous creation of two pions, a π+and a π−. Both the pions have

a mass of 2.49 × 10−28kg. Suppose that a kaon moving in the +x direction decays by this process with the π+ moving oﬀ at speed 0.9c and the π−at 0.8c.

(a) What was the speed of the the kaon before decay?

(b) In what directions do the pions move after the decay?

mass of kaon = 8.87x10^28 kg

mass of both pions = 2.49x10^-28 kg

u of pion+ = 0.9c

u of pion- = 0.8c

I solved part a) and found that the speed of the kaon before decaying was approximately 0.437c

and just need a little help with the second part

2. Relevant equations

momentum in x direction =

γ_{k}m_{k}u_{k}= γ_{+}m_{+}u_{+}+ γ_{-}m_{-}u_{-}

momentum in y direction =

0 = γ_{+}m_{+}u_{+}- γ_{-}m_{-}u_{-}

where the + and - subscripts are for the + pion and - pion and k is for the kaon

3. The attempt at a solution

so basically i plugged in what I knew, and reduced everything to this:

Momentum in x direction =

4.30 = 5.13cosθ_{+}+ 3.33cosθ_{-}

Momentum in the y direction =

3.33sinθ_{-}= 5.13sinθ_{+}

i have 2 thetas and I'm not really sure how to go about finding the angles... I cancelled the c's and the x10^-28 from both sides to make it a little bit nicer but I'm just stuck... here any advice would be great :)

PS: for my past life, i seen people dividing equations by each other a lot cancel things out. If anyone can also provide an explanation to what is really happening, it would be nice too.

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# Homework Help: Modern Physics Momentum and Trying to find the Direction of Decayed Particles

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