It's somewhat counterintuitive how much energy can be in something moving so slowly. I say somewhat, because when you're up close it's much more obvious, but you're right that on a video it doesn't look like much.
This disconnect happens with boats quite a lot. For example, I can, by myself, pull a 45 foot grand banks trawler in shallow water. I know because I've done so.
But at even very low speeds, I cannot stop it from hitting a pier. I have not tried to do this, but every harbor master has a bunch of stories about people trying to do so and getting a leg or an arm or something squished and pulverized.
People who are not boat people rarely recognize these sorts of dangers, which is why so many get hurt on boats. "I can push us off the dock, so I can definitely keep us from hitting it." Nope, Sir Isaac Newton says you're wrong.
To anyone reading this who isn't an experienced boater:
If you are invited onto someone else's boat, sit down and shut up during docking, don't talk to friends, let the captain concentrate. Don't help, if the captain wants you to do something, they will let you know. If you think you know better than the captain, and this advice is unknown to you, you don't know better. Being a good guest during docking shows experience and helps get an invite back.
Try docking a sailboat on a river. Then slow isn’t an option, since the current will sweep you away in a heartbeat. The key here is planning ahead, including a plan for what to do when you don’t get it right. And you won’t, on the first couple of attempts. I’ve seen it in action, totally hair raising to watch.
This is great advice. For myself, docking in windy situations can be nerve racking. The old adage is to only dock as fast as your willing to hit the pier, and for me this means slow as hell.
I always let guests know exactly what I want them to do, and to your point, it's mainly to sit tight and let me focus.
Similar to stay quiet if the car is about to merge into traffic. But with a boat the stakes are 100,000 times greater due to the huge momentum and that it would be gliding and not slowing down like a wheeled vehicle on land.
Landlubbers are accustomed to momentum (p = mv) behaving in a certain way instinctively from years of experience, where the heavier something is, the more frictional force against it from the ground, and therefore the mass behaves a certain way. This breaks down once the expected friction changes a lot, e.g. trying to stop a moving car or, like you said, a boat in water. I'd imagine it's the same thing in space, where a slowly-moving but massive object would surprise someone at their inability to stop it.
This hit me a a bit ago - you can't really tell how big ships are if you just see pictures of them on sea. I recently hit this in real life. Yeah it's a ship. Oh. It's like 3 - 4 times as tall as I am above water. And it goes 2-3 stories down. And holy hell, a crows nest 30 meters up is... really high up?
And we got the good tour, because we had a severe storm warning as we visited that ship - the kinda storm in which gusts stop you in your tracks and forces you to lean into it to not fall over. Was a great experience. I wouldn't want to be up there with that kinda wind.
And this was a medium sized clipper, somewhat on the small size.
And based off of that, I kind of want to see a retired battleship or an aircraft carrier. Because now I have an idea of how dumbfounded I'll be at those kinda dimensions. It just doesn't appear that big on photos!
The best place I've seen huge ships is Hamburg. People sit and picnic on beaches along the river in the summer, and enormous container and car carrier ships go past.
We had a team we work with a lot over here in HH and went on the treasure hunt on the Rickmer Rickmers as an event. That was very nice - they spread a bunch of little puzzle boxes across the ship so you can search for these, walk through the museum and look at stuff. And the puzzles were neat as well - you'd use the compass the actual helmsman used back in the day to figure out where east is to find some clue, count pests in cargo and such. Very recommendable and a lot of fun.
We just didn't climb up the ropes in winds that almost pushed you over on foot, haha.
The same go for cars. I was hit by a car which was already slowing down but over ran the line and hit me. The car couldn't have been going more than 10 mph but it was enough force to fracture my knee (the fracture type is also colloquially known as a bumper fracture).
But in this case with slow speed, it's the massive (literally) amount of mass of the cargo ship that gives it an un-intuitively large amount of energy.
To your point, it is mass. Most people don't understand mass on water. At 1 knot the ship would do the exact same damage, topple the support and drop the bridge.
Nitpick: squaring makes numbers greater than 1 bigger, and numbers smaller than 1 smaller. In this case we're squaring something with units, and we can't say the input is greater or smaller than the output, because they have different units. What we can say, is that v^2 curves upward: it grows faster with increasing v, and slower with decreasing v.
