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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
→ -cos2 x + cosx + 1 = v/v''
→ cos2 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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