Finding the energies of 2 photons from a decay of a travelling mass

[Aaron7]

Homework Statement

Mass M traveling at v=c/3 decays into 2 photons in x and -x directions.

Mass M orginally formed by mass m traveling at v=3c/5 hitting a stationary mass m.
This gives M v=c/3 and M=3m/√2.

Homework Equations

E=K + mc^2

p = gamma m v
E = gamma m c^2

K = (gamma -1) mc^2

E^2 - p^2 c^2 = m^2 c^4

The Attempt at a Solution

I am confused how the photons form from a moving mass. How would I find out the ratio of the energies of the photons?

 

[collinsmark]

Use your E² - p²c² = m²c⁴ formula to find the relationship of a given photon's momentum and its energy. Set m = 0. Then solve for p.

Then set up the following simultaneous equations (noting that the photons fly off in opposite directions on the x-axis):

• (Energy of one photon) + (Energy of the other photon) = (The original energy of the system)
• (|Momentum of one photon|) - (|Momentum of the other photon|) = (|Original momentum of the system|)

"Original energy of the system" above is the original total energy of the system; not just its kinetic energy. You have two equations and two unknowns. You can take it from there.

Mass M orginally formed by mass m traveling at v=3c/5 hitting a stationary mass m.
This gives M v=c/3 and M=3m/√2.

Your above calculations kinda worry me. Is this intermediate step something you are explicitly told to calculate? If so, I don't think it's correct: According to my calculations, (total) energy and momentum are not conserved in your calculations (as they should be). If you are not required to perform this intermediate step, then I don't think it's necessary.