Hmmm
I can see a checkmate in 3, but the black king needs to make a wrong move for that to happen.
Rh1 moves to h8
Black king is forced to take the pawn in g3
Then R moves from h8 to g8
king is forced to move to h2, h3 or h4. If he doesn't move to h2, then the other R moves to h1 and it's...