A 4kg ball moving at 8m/sec

Conservation of momentum: total momentum before = total momentum after

Momentum = mass x velocity

So before the collision:

4kg x 8m/s = 32

1kg x 0m/s = 0

32+0=32

Therefore after the collision

4kg x 4.8m/s = 19.2

1kg x βm/s = β

19.2 + β = 32

Therefore β = 12.8 m/s