Artificial gravity ship: Floor?

[Nugatory]

So if one were to jump "really hard", would that enable one to land on a different spot than the one you jumped off from?

Yes, because the higher your jump and the longer you spend in the air traveling a straight line while your jumping-off point is following the curved path, the less accurate the small-angle approximation becomes.

Something similar happens when you jump on the curved surface of the earth. You don't notice or worry about the rotation and curvature of the Earth when you make a normal human-sized jump. But if you're aiming very long-range artillery (the artillery shell is "jumping" many kilometers and spending an appreciable time in flight) you do.

 

[sophiecentaur]

So if one were to jump "really hard", would that enable one to land on a different spot than the one you jumped off from?

However high you jump there is a difference between your traveled distance and how far the floor has traveled by the time you land. The difference is increasingly relevant, the higher you jump.