Shipwreck survival

[Anthony]

Originally Posted by Agemegos

That sounds more like standing at sea level (i.e. with any eye height of five and a half feet) than immersed at sea level (i.e. with an eye level only a few inches above the waves).

Horizon distance is typically given as 3.57 km * sqrt( height / 1m ), so 7 miles is too far even for someone standing up, and for someone swimming would be more like 1-1.5 km. However, you can see things that are over the horizon if they're tall enough -- if we assume 1.3 km horizon from swimming, and 10 km for the target (total 11.3 km, or 7 miles) the object needs to be about 8 meters tall to be visible, which is a decent-sized tree but not impossible, and mountains would be visible quite a bit farther, probably out to the range at which atmospheric haze wipes them out.