You don’t rotate with the earth, instead you continue on a straight path, and accelerate downward due to gravity.
It’s just that, for short distances, earth surface can be approximated as flat, and rotation along this surface is not that different from a straight line.
But for long distance, this approximation does not hold. If you fire an artillery shell, the shell follows a parabolic path, but the target does not move on a straight line during the flight time. This will end up having an effect over long distances, so you actually need to account for earth rotation.
You don’t rotate with the Earth when you are off the ground, lets forget about air for a moment. When you jump the tangential velocity you had from the Earth’s rotational is conserved and so you start moving in a straight line. However, the Earth is huge and so that for that little time you spend in the air the Earth rotates a very small angel. So basically the difference in velocity between the point you jumped from and your velocity is practically 0.
Of course if you want to measure this effect you need to get clever and introduce some oscillation where this difference can add up. That’s sorta how a Foucault pendulum works.
If we include air so basically why isn’t a hot air balloon effected at all is because the air it’s suspended in does rotate with the planet. Why? Well imagine if it didn’t that would introduce friction between the ground and the surface, I think a huge space rock has more inertia than the thin atmosphere so the bottom layer would speed up to match the rotation and because the air has viscosity this will continue upwards until the atmosphere mostly uniformly rotates with the Earth. So of course a hot air balloon won’t be effected. Basically everything that uses the air to suspend itself.
The air, you and the earths crust is all moving, rotating.
To expect anything else than it continuing to move would be odd. Imagine if when you threw something in the air it would suddenly not follow earths rotation. So a baseball would suddenly start flying westward at 1000miles per hour the moment it left your hand. That would be freaky as hell.
If you’re in a closed moving vehicle and throw something directly up in the air, you’ll still be able to catch it. That’s because the object you threw is still moving at the speed of the vehicle, as is the air inside it. The same happens with the Earth itself. You, the air, and everything else that was recently in contact with it, is moving at the same speed as the Earth. So, of course it’s going to rotate with the rest of the planet.
If you jump straight up, you keep whatever horizontal velocity you started with.
As for planes, their speed while flying is in relation to the air, and while the air does move in relation to the ground(i.e. wind), it’s relatively slow compared to the rotation of earth around its axis. Because air has friction with the ground.
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