Relativistic dynamics-collision problem

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SUMMARY

The discussion focuses on a relativistic dynamics problem involving an elastic collision between two particles. Particle 1, with mass m1, collides with stationary Particle 2, mass m2, resulting in Particle 1 moving perpendicularly to its initial direction. The angle θ between the movement direction of Particle 2 after the collision and the initial direction of Particle 1 is defined by the equation tanθ = |p'1| / √(2T1m1 + T1²/c²), where T1 represents the kinetic energy of Particle 1 before the collision and c is the speed of light in vacuum. Additionally, the momentum vector length of Particle 2 post-collision is given by √(|p'1| + 2T1m1 + T1²/c²).

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I WOULD BE VERY THANKFUL IF ANYONE COULD PLEASE ME WITH THIS PROBLEM! :)

Particle 1 with mass m1 encouters elastic collision with particle 2 which has mass m2
Assume that particle 2 is stationary before collision.
And movement-direction of particle 1 after collision, is perpendicular to the movement-direction before collision.
Let T1 symbolize kinetic-energy of particle 1 before collision
And p'1 momentum of particle 1 after collision

a) show that the angle between the movement-direction of particle 2 after collision and movement-direction of particle 1 before collision if θ where
tanθ = lp'1l / sqrt(2T1m1+T1^2/c^2)
b)show that after collision, length of the momentum-vector of the particle 2 is
sqrt( lp'1l+2T1m1+T1^2/c^2)
 

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what does c refers to in the ans.
 
c= The speed of light in vacuum
 

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