Before the collision, the two balls' total momentum is
(1 kg) (+1 m/s) + (1 kg) (-1 m/s) = 0
After the collision, the combined balls have velocity v such that
(1 kg + 1 kg) v = 0
since momentum is conserved. Equivalently,
(2 kg) v = 0
It follows that v = 0, meaning after impact the balls are stuck together and motionless.
