“A hobby missle isn’t launched from 35 miles off-shore...”
Actually, if you built one that size, you might do exactly that to avoid getting arrested for doing it on land.
So you take you boat out....
Missile that size, with that kind of fuel would roast a pleasure boat on take-off.
http://www.the-rocketman.com/go-fast.html
It would take a good sized boat to do it on water!