I was thinking the same thing...and who says we would have to send people to deliver the trash? I'm sure we can develop something with navigation to go straight to the black hole...considering the hole's gravitation pull, with a big push from Earth, I think the trash can find its way easily.
By the way, the closest black hole is only about 1600 light years away. So...if we develop the ability to travel at the speed of light, it would only take us about 1600 years to get there. And taking into consideration that time is relative, we would age much slower -- but I'm not sure if we would make it to the end of 1600 years even if we aged tremendously slow...but why would we even send people to the black hole?? Why survive 1600 years just to be obliterated? Come on.