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In perfectly inelastic collision the two bodies stick together after
they have made contact and, as consequence, both have the same final
velocity (fig.5.12)

Conservation of the impulse alone is sufficient to permit us to compute
the final velocity if the masses and initial velocities are known

before

collision

after

collision

Figure 5.12

Before collision impulse of bodies is equal to

  
p  m v  m 2 v . (5.40)
20
10

After perfectly inelastic collision these bodies moves like one integral
unit, so that
 
p  ( m  m 2 v  ) . (5.41)
1
According to conservation impulse

  
m 1 v  m 2 v 20  m  m 2 v , (5.42)
10
1

velocities of these bodies after perfectly inelastic collision are equal.In
vector form we can write it as
 

 m v  m v
v  1 10 2 20 . (5.43)
m  m 2
1
or in scalar form on X- component

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