# Answer to Question #4192 in Mechanics | Relativity for Nantu

Question #4192

Particle

*A*of mass '**m**' has initial velocity**v**. After colliding with a particle*B*of mass & '**2m**' the particles have the following paths*B*makes an angle**45**degree while*A*makes an angle**X**. & First, &*A*was moving straight. & Find*.***X**Expert's answer

Projections of momentum

mv=2mv'cos45 + mv'' cosx

v=2v'cos45 + v''cosx

0=2v'sin45 - v''sinx → 2v'=(v''sinx)/sin45

v=(v''sinx)/sin45 cos45 + v''cosx →

v=v'' (sinx+cosx)→ v''(1-cos^2 x + cosx)=v

→ -cos

→ cos

→ cosx=1/2 - √(1+4(1+v/v')/2

mv=2mv'cos45 + mv'' cosx

v=2v'cos45 + v''cosx

0=2v'sin45 - v''sinx → 2v'=(v''sinx)/sin45

v=(v''sinx)/sin45 cos45 + v''cosx →

v=v'' (sinx+cosx)→ v''(1-cos^2 x + cosx)=v

→ -cos

^{2}x + cosx + 1 = v/v''→ cos

^{2}x - cosx - (1+v/v'')=0→ cosx=1/2 - √(1+4(1+v/v')/2

**x=arccos 1/2 - √(1+4(1+v/v'') )/2.**
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