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Oblique Collision of Two Bodies

Total initial momentum (before collision) of the two bodies in x direction

= m1 u1 cos θ1 + m2u2 cos θ2

 

And total final momentum (after collision) of the two bodies in x direction

= m1 u1 cos ϕ1 + m2u2 cos ϕ2

 

The momentum is conserved in any direction (here in x direction)

: = m1 u1 cos θ1 + m2u2 cos θ2= m1 u1 cos ϕ1 + m2u2 cos ϕ2