The Rock can defeat the king
Can 1 Rock defeat King?
how large is this rock? and from what angle do you aim at the king
Rock is at Re5 and King is at Ke8 with the Pawn at f7
Maybe the king tries to run down the e-file and trips over the rock.
The rock defeats the king.

One rook alone is not sufficient to checkmate the opponent's king.
You need the assistance of a friendly piece like the king.
i think its not possible to defeat a king with one roook but possible with two rooks