Pretty Dynamics of Block and Hemisphere

A rough Hemisphere of $\large x^{2}+y^{2}+(z-1)^{2}=1,\mu=0.3$
and a small block of mass $m=0.5$ ( consider it as a particle only ) placed at point $S$
where $S=(-1, 0,1)$ and is given a velocity of $v=0\vec{i}+8\vec{j}+0\vec{k}$ at $t=0$ .
Consider that the hemisphere is fixed at origin $N(0, 0,0)$ .
Find the time taken by the block to stop for the first time.

Details and Assumptions
1) $g=10$ , gravity is acting downwards $(-\vec{k})$ , and it's uniform.
2) Neglect air resistance
3) Consider everything in SI units.

This problem is dedicated to my respected teacher Steven Chase .

The problem is original.