(Old photographer joke: You're shooting by a lake on a cloudy day and you happen on someone drowning, and have to choose between dropping your gear to run to the rescue and getting a shot to sell the local paper. So - what f-stop do you use?)
I'd be more concerned about shutter speed. If the drownee is flailing their arms, dragging the shutter slower might yield a more dramatic look with the motion blur. Too high of shutter speed so the action is frozen might look more like someone rehearsing their part in a synchronized routine.
Keeping the subject in focus is more important as a decent telephoto will get you an out of focus background. Unless you're just a dick and use a wide angle but wade out into the water to get a decent framing.
I would use fastest aperture I can that is still sharp and just shot a bunch of frames very quickly in hopes I can get arms in just the right, dramatic position.
As to whether to shoot wide or tele, if you feel you have enough time try to get subject to fill the frame first, while he still looks lively, and then quickly change the lens to get some additional shots with the background.
I estimate full 1/3rd of entire training was devoted exclusively to getting a person back on the ship if they happened to fall into water while underway.
It is said "people do not splash" because if you are focused on looking for flailing hands and splashing water and shouts for help then your are missing most people that drown.
But it doesn't mean people don't shout and don't flail. They do. Just not most of the time.
conclusion: The drowning person is a project manager.
How did this captain know—from 50 feet away—what the father couldn’t recognize from just 10? Drowning is not the violent, splashing call for help that most people expect. The captain was trained to recognize drowning by experts and years of experience. The father, on the other hand, had learned what drowning looks like by watching television."
2013 Slate article: https://slate.com/technology/2013/06/rescuing-drowning-child...
Someone who is not exhausted and not technically drowning yet but who will be if left for another 10,15,60 or whatever minutes does have the ability to yell and splash.
also, digital cameras could just compensate slower f-stop with higher ISO if necessary
(And thank you all for bringing the back half of the joke in such inimitable style!)
(I'm never one to shy away from answering obvious rhetorical questions in a joke)
Actually you can do the same with film. You just push it in processing.
Whether film or digital it results in grainy image, that's why I actually mentioned it.
Pros don't bring grainy images of drowning people.
So I'm just going to come out and say claiming that pushing the ISO and introducing noise during a daytime (albeit cloudy) shoot and pushing the ISO a few stops to counter stopping down is fake news and scaremongering.
Can be pretty hard to see, but no absolute about flailing
(On iPad I had to stop loading before page would show the random video, YMMV).
Though to be fair, he would not have been able to rescue the said individual.