Each croquet ball in a set has a mass of 0.50 kg. the green ball travels at 10.5 m/s and strikes a stationary red ball. if the green ball stops moving, what is the final speed of the red ball after the collision?

Momentum conservation law!

mv before collision = mv after collision

momentum of green ball before collision 0.5 kg * 10.5 m/s + momentum of red ball before collision 0.5 kg * 0 m/s = momentum of green ball after collision 0.5 kg * 0 m/s + momentum of red ball before collision 0.5 kg * unknown speed in m/s

0.5*10.5 + 0.5*0 = 0.5*0 + 0.5*v

v = 10.5 m/s