Its just a collision

I don't know whether my solution is correct or not, feel free to report any flaw.

I will place the values later in the answer.

velocity of ball after collision is $e\sqrt{2gh}$

Impulsive force from normal causes change in momentum of the ball.

$J_{N}=N.dt=$ $final$ $-$ $initial$ $momentum$ .

As after collision velocity of ball is in opposite direction so

$N.dt=me\sqrt{2gh}-(-m\sqrt{2gh})$

( after replacing value of $e$ )

$N.dt=1.5m\sqrt{2gh}$ ................................... $(1)$

The impulsive frictional force (denoted as $f$ ) will cause change in momentum of block.

$J_{f}=f.dt=-m \Delta v$

(minus sign because velocity decreases)

Using

$f=\mu_{k} N$

$\mu_{k}N.dt=-m\Delta v$

From $(1)$

$\mu_{k}\times 1.5m\sqrt{2gh}=-m\Delta v$

putting values

$\Delta v=-0.2\times 1.5\sqrt{20\times 42.05}$

$|\Delta v|=|K|=8.7$