In order to determine the speed of the entire assembly, we employ conservation of momentum. Momentum p = mv where m is the object's mass and v is the velocity.
The putty ball's initial momentum p1 = 0.3kg*6m/s = 1.8 kg*m/s
That momentum is conserved, so the momentum of the new system having mass 0.3 kg + 1.2 kg = 1.5 kg is:
1.8 kg*m/s = 1.5kg*v. Solving for v, we find that the velocity is 1.2 meters/second.
