This question involves the concepts of the law of conservation of momentum and velocity.
The velocity of the eight ball is "5.7 m/s".
According to the law of conservation of momentum:
where,
m₁ = mass of number three ball = 5 g
m₂ = mass of the eight ball = 6 g
u₁ = velocity of the number three ball = 3 m/s
u₂ = velocity of the eight ball = - 1 m/s (negative sign due to opposite direction)
v₁ = final velocity of the three number ball = - 5 m/s
v₂ = final velocity of the eight ball = ?
Therefore,
(5 g)(3 m/s) + (6 g)(- 1 m/s) = (5 g)(- 5 m/s) + (6 g)(v₂)
<u>v₂ = 5.7 m/s</u>
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Learn more about the law of conservation of momentum here: