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

[RadiantL]

Homework Statement

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

Homework Equations

momentum in x direction =
γ_km_ku_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

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 canceled 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.

 

[mark726]

To solve for the angles, you can use trigonometric identities to eliminate one of the thetas. For example, you can use the identity sin^2θ + cos^2θ = 1 to solve for one angle in terms of the other. Then, you can substitute this into one of the equations to solve for the remaining angle.

As for dividing equations, this is a common technique in mathematics called "elimination" or "substitution." It involves using one equation to solve for one variable, then substituting this value into another equation to solve for another variable. In this case, you can use the equations for momentum in the x and y directions to eliminate one of the thetas and solve for the other.