[midoridensha]

A few problems with this analysis:

1. Humans aren't going to survive in space for 10 years. It's questionable that they'd even survive a trip to Mars without getting riddled with cancer from the cosmic radiation. Sure, if you built a big enough ship to provide some really effective shielding, it's technically possible, but that ship would be enormous and far beyond our current capabilities. I don't think it's feasible at all to launch such a ship from Earth; it would need to be assembled in space.

2. Project Orion is just an idea on paper; it's not within current technology, because no one ever built it. We don't "have the technology" at all. We don't even have the technology to land humans on the Moon. We did decades ago, but we no longer do: all the people who knew how to do that are retired or dead, so we'd have to start over. Of course, we can build powerful rocket motors easier now since we do so regularly now, so building equivalent Moon-landing capability is no longer as difficult as in the 60s, but a lot of things would have to be partially re-invented (e.g., the lander itself, the rover, etc).

3. Does your time estimate include the time needed to decelerate, so the ship doesn't just zip by the black hole with barely any time to collect data? (And if there's people on this ship, they might want to return to Earth...)