I am arriving in Naples, Italy for one day (7am - 7pm). Is it possible to take the hydrofoil at 9am from Naples to Sorento take the bus down to Positano, then eat luch, and take a ferrie / hydrofoil back to Sorrento in time to catch the train to the pompii ruins. Then back to Naples in time to eat at the birth place of Pizza.
In 12 hours, sure it might be technically possible, but you're going to spend a great deal of that time standing in line for transportation or riding it, and not too much enjoying the sights you came to see.
Dennis, You can do it but I suggest to make better use of your time by taking the train in Naples to Pompii first. Then head to Sorento...from there take the bus (beautiful views) to Positano..you can take the hydrofoil back to Naples and have pizza.