---- this below is close but not exact -----
The 5" 38 Cal gun shoots at roughly 2,600 ft/s with a ceiling of around 37,000 ft. On a straight shot (straight up) it will take 5.7 seconds to reach it's target. to hit a target moving at 254 mph (in theory) you would have to fire 5.7 (more realistic would be 6-6.5 seconds) seconds in front of the target. that's if you managed to keep it tracked in front of you while the ship is rolling in the ocean with momentum (god forbid if it's negative momentum)......
2,600 ft/s (790 m/s) new; 2,500 ft/s (760 m/s) average
every 10k ft you're looking at about 4 seconds if the velocity were to stay the same (which we know it doesn't). I had a whole bunch of info yesterday, but it is easier to get this chart from Wiki. It's right so long as it hasn't been changed from since then...
Range with 55.18 lbs. (25.03 kg) AAC Mark 49 (792 mps)
10° 9,506 yards (8,692 m)
15° 11,663 yards (10,665 m)
20° 13,395 yards (12,248 m)
25° 14,804 yards (13,537 m)
30° 15,919 yards (14,556 m)
35° 16,739 yards (15,298 m)
40°17,240 yards (15,764 m)
45° 17,392 yards (15,903 m)
AA Ceiling 37,200 feet (11,887 m)
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The elevation range are something along the lines of (-5º)-(85º)
When coupled with the Mark 37 Fire Control System, used on most US warships built between 1939 and 1946, these guns were also effective in the AA role. For example, during gunnery trials in 1941, USS North Carolina (BB-55) was able to repeatedly shoot down drone aircraft at altitudes of 12,000 to 13,000 feet (3,700 to 4,000 m), about double the range of the 5"/25 (12.7 cm) AA Mark 10 used on older ships.
http://www.navweaps.com/Weapons/WNUS_5-38_mk12.htmOne day it will happen and bombers will curse while fighters cheer.