Relativistic dynamics-collision problem

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The discussion focuses on a relativistic dynamics problem involving an elastic collision between two particles, where particle 1 collides with stationary particle 2. It is established that after the collision, the movement direction of particle 1 is perpendicular to its initial direction. The first part of the problem requires demonstrating the relationship between the angle θ and the momentum of particle 1 after the collision, expressed as tanθ = lp'1l / sqrt(2T1m1 + T1^2/c^2). The second part involves showing that the momentum vector length of particle 2 after the collision is given by sqrt(lp'1l + 2T1m1 + T1^2/c^2), with 'c' representing the speed of light in a vacuum. This analysis highlights the interplay between kinetic energy, momentum, and relativistic effects in collision scenarios.
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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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