It’s a video game where there’s a mission in which you have to destroy a missile silo. But the silo tracks you and fires a missile right at your location every several seconds. It makes a loud boom sound in the distance every time it fires. And it stops firing once you get to a close enough distance.
I’m pretty sure it’s an open world game, perhaps a bit like Just Cause? This might be some Mandela effect shit because I’m not even 100% sure this game exists.
There’s part of an area in Half Life: Opposing Force that has something like this. You later end up using the cannon yourself to open up the path forward.
You could also be thinking about a couple of parts of the original Half-Life as there are a couple of times with mortar fire (including the ability to use them yourself at one point), and there’s definitely at least one rocket launch silo in the game.
Depending on how strong your recollection or how muddled your memories these could be a match.