We want to get the final velocity of two balls after a collision.
The final velocity of the combined ball is 2.4 m/s.
We know that a ball of 8kg moves with a speed of 3 m/s and impacts a 2kg ball at rest.
Here we need to use conservation of momentum (mass times velocity). This means that the momentum before the impact must be the same as the momentum after the impact.
The momentum before is given by:
P = (8kg)*3m/s + 2kg*0m/s = 24 kg*m/s
After the impact, the two balls become one and move with a velocity V, so the final momentum will be:
P' = (8kg + 2kg)*V = 10kg*V
By conservation of momentum we must have:
24 kg*m/s = 10kg*V
(24 kg*m/s)/(10kg) = V = 2.4 m/s.
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