Please show all work and all formulas used I am really tryin

Please show all work and all formulas used I am really trying to learn

A particle of mass M is moving in the positive x direction with speed v. It spontaneously decays into 2 photons, with the original particle disappearing in the process. One photon has energy 233 Me V and moves in the positive x direction, and the other photon has energy 21 Me V and moves in the negative x direction. What is the total relativistic energy of the particle before its decay? What is the momentum of the particle before its decay? Find the mass M of the particle, in units of Me V/c2. Find the original speed of the particle, expressed as a fraction of the speed of light.

Solution

a) Observed length according to Mary:

L₀= L_r(1-v²/c²)^1/2 = 2450(1-(0.74c)²/c²)^1/2 = 2450*0.672 = 1647.886 m

b) Observed time can be stated as: t₀ = t_r/(1-v²/c²)^1/2

t₀ is 0.740, t_r is 1

1/0.740² = 1-v²/c² = 1.826

v = (0.826c²)^1/2 = 0.908c m/s

So according to Mary, time interval between the bow(front) of the ship passing her and the stern(rear) of the ship passing her is 1647.886/0.908c = 604.95*10^-8 s

c) So according to Jim, time interval between the bow(front) of the ship passing Mary and the stern(rear) of the ship passing her is 2450/0.908c = 899.41*10^-8 s