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Modern Physics Momentum and Trying to find the Direction of Decayed Particles

  1. Oct 14, 2012 #1
    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 =
    γkmkuk= 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.
     
  2. jcsd
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