Well, as the earth rotates on its axis, it's not just land that spins, but also all the water on earth (as well as the air in the earth's atmosphere!). So if someone were to float in water, the person would rotate along with the water and earth. (This is easy to check - the surface of the earth is moving at hundreds of miles an hour relative to its center, so if you didn't move along with the earth when you went swimming, you'd see the earth zipping by you!)

Interesting question! Let’s consider an example of a rocket that was designed to fly straight up and be capable of maintaining a steady altitude. On the ground there are effectively two forces acting upon the rocket: gravity downward and a horizontal force via friction. These combined forces create an angular velocity of the rocket “orbiting” the earth at exactly the same period as an earth day. As soon as the rocket takes off, it loses contact with the ground, and assuming no atmospheric friction, the only force acting upon it is gravity. However, because of its initial horizontal velocity (due to the rocket already spinning around the earth before taking off), gravity acts as a centripetal force to keep the rocket (mostly) stationary one point above the ground.

Now the rocket begins to climb higher in altitude. In order to keep up with the orbit of Earth’s surface, the rocket’s angular velocity around the Earth needs to match. Recall that angular velocity ω = v/r . As the altitude r increases, linear velocity v needs to increase proportionally. Unfortunately, there is no horizontal force to accelerate linear velocity. Additionally, gravity is an inverse function of distance between two objects, so the higher the rocket is, the weaker the gravity acting on it is. This means that the rocket is incapable of accelerating at the necessary (linear) velocity to keep in one place above the surface. Ultimately the rocket will see Earth pass beneath it as its orbit slows down.

The water that you are floating in is being carried along with the rotation Earth, and you along with it, so you move with the Earth. This is because you are suspended in the water, so the water is able to exert force on you to keep you not moving with respect to the water. If you were hovering in place, however, the Earth would rotate underneath you.