Destructive rook sacrifice on h3

Destructive sacrifice - "sacrificing material to destroy the pawn cover or other protection around the enemy king. Usually a point of no return" (dictionary).

Many of us are familiar with the bishop sacrifices - Bxh2/h7/h3/h6/... etc. Rook sacrifice is a bit less common, maybe because it takes time and effort to get the rook into the striking position.

The first example is from my online game. My time was running out, and  after I made move Qd6-e6, I had 7 seconds left. Luckily for me, my opponent didn't suspect anything and played c4-c5.

After Rxh3+, gxh3, Qxh3# I still had a few seconds.

Second, more complicated example is also from my online game. Rxh3+ with mate in 8 - can you calculate it?