Most people think U-boats were designed to sink ships with torpedoes; they were actually designed to sink them with the deck gun (they couldn’t carry enough torpedoes to operate very effectively at any long range). Early in the war, the U-boats would surface next to the freighter, warn the captain (and let the crew abandon ship), then sink it with shells below the waterline.
As Britain fought back by arming freighters and using decoys (Q-ships) and escorts, the U-boats couldn’t risk surfacing like that (they were easy targets with thin hulls); the war became more brutal at that point.
There was one instance (possibly before the US was in the war) where people on a beach in Florida watched a U-boat sink a freighter; IIRC the U-boat was on the surface between the beach and the prey. Incredible.
The particular event you're describing took place off of Daytona Beach, I believe it was.
From the Univ of South Florida Museum of WW II:
German U-Boats sank over twenty-four ships off of Florida's Atlantic and Gulf Coasts. Many ships could be seen burning from areas along the coast by Floridians and tourists. In late February 1942, German submarines attacked four merchant ships right off the east coast of Florida near Cape Canaveral.
All of these attacks took place after we entered the war. The Kriegsmarine had an insufficient number of long-range submarines to mount patrols off the U.S. coast until shortly after war was declared.
The Florida coast and off Cape Hatteras were favored hunting grounds for months, as merchant ships traveled without escorts and we weren't equipped to mount effective anti-submarine patrols.
The formation of the Civil Air Patrol (CAP) was one of the outcomes of this situation. My father, who wasn't eligible for the draft and owned a light plane, flew from Oklahoma down to Galveston, TX and was part of a patrol unit stationed there.
"The most dramatic sinking in Florida waters took place the night of April 10, 1942, when U-123 torpedoed the tanker Gulfamerica off Jacksonville Beach. The resulting fiery explosion was clearly seen onshore and curious crowds gathered to view the ship's destruction and looked on in shock as the German submarine surfaced and fired its deck gun at the tanker. In response to the Gulfamerica sinking, in which nineteen crew members were lost, Governor Spessard Holland ordered a blackout of lights that could be seen at sea and might silhouette passing ships."