If you sink an object and then let go then it accelerates upwards. What if I sank something a very long way (say a mile or so)?

I've read in New Scientist about the potential of using supercavitation to travel very fast through water.

So what’s to stop me attaching a lightweight projectile onto a big rock with a piece of string which will detach at a certain depth, dropping it off a boat and firing something into space?