It's been surmised by flat-earthers that if the Earth is moving then we should be able to lift off of the ground in a balloon and the ground should travel below us. Others have suggested that flights going with the rotation of the globe should be impossible because the globe rotates at 1000 mph but planes only fly at about 500 mph. These theories are both part of the same false premise which is that as soon as we leave the ground we should cease to travel in the same direction and speed as the Earth.
Before getting into the meat and potatoes of this issue we must establish that IF the Earth is rotating then we are all rotating with it at the same speed. If we are traveling at a certain speed, Newton's 1st law applies. Namely, that an object in motion will remain in motion until acted upon by an outside force. In other words, we will remain in motion (on the earth) unless something exerts a force upon us. With that in mind, let's address a few questions.
Why can't I feel myself moving?
The reason why we don't feel the motion is because we don't feel constant motion. We only feel changes in motion or changes in direction. For example, we feel our cars acceleration but once we are at speed we don't feel anything other than some road vibrations (an outside force). Once we are at speed we can feel G-Forces when we go around a bend because it's a change in direction and our bodies in motion want's to remain in motion, in the direction we were traveling.
At this point, some of you are wondering why we can feel ourselves going around a turn but not feel the Earth rotating, which is technically a change in direction. The short answer is that G-Forces are the result of two factors. The first is speed and the second is the distance of the radius. That is why going around a long bend at 55 mph feels differently than taking a highway on/off-ramp at 55 mph. Calculating the force is rather simple but we won't do that in this article. An entire article has already been done on this subject and can be read at the following link.
The other reason why we don't feel the motion of the globe is because it's movements are incredibly smooth and uninterrupted. But we DO feel some of Earth's motion. For example, we feel earthquakes. Even though an earthquake only moves a tiny bit compared to the rotation of the Earth. The reason why we feel it is because it's a vibration, not a motion. A vibration is a rapid succession of directional changes. However, it's not really fair to include an earthquake in the same category as Earth's movement because an earthquake is actually moving along with the Earth.
If the Earth is rotating, why do I rotate with it when I jump or leave the ground?
To the logical mind, it seems to make sense that if we leave the ground, we should cease to spin with the earth. After all, we are no longer connected to it, right? Not exactly. There are two factors we are forgetting. First, even if we did disconnect from the spinning ground we are going to remain in motion unless acted upon by an external force (remember Newton?). What force is present to act upon us? The only force present would be that of the atmosphere but even that is moving with the globe. There are jet streams the travel across the face of the globe but we are talking about 10-40 mph, relative to the 1000 mph that they are traveling in the direction of the globe. If the atmosphere acted upon us it would only be 10-40 mph and it's just a breeze acting upon any given object; not exactly a strong force.
We can demonstrate this principle by tossing a ball inside of a sealed vehicle. Inside the vehicle nothing can act upon the ball. However, if we throw the ball out the window we can see that the ball want's to travel in the same direction and maintain the same speed, but it's acted upon by the atmosphere and then eventually gravity and friction from the ground. Example below.
If the flat-earther theories were true then the ball would just immediately get left behind as it exits the car. Now imagine that the wind working against the ball was moving in the same direction as the car and at the same speed. The ball would actually keep pace with the car until it hit the ground.
What about the planes flying the same direction as the Earth spinning?
The principles already discuss apply to planes also. Any plane in motion when it leaves the ground is already going the same speed and direction as the rotation of the earth and since the atmosphere is traveling at relatively the same speed and direction, there is nothing acting upon the plane to change it's direction. This theory can be replicated by throwing a ball inside of a moving vehicle from the back to the front. The atmosphere inside the car is moving with it so the ball is able to move through it as if it were not moving because the ball is already moving at the same speed as the atmosphere inside the car. However, the atmosphere outside the car is a different story.
Once an outside force acts upon a moving object we can calculate what will happen to the object by using some basic physics. In school most people learned about relative velocity and probably learned to calculate things call vectors.
I could go on and demonstrate vector math but it won't make for a very exciting reading. However, this video will help the reader to understand how vectors work. My first physics teachers made us do so many vectors that we actually nicknamed him vectorman. But I am glad today that he did because vectors are the building blocks for physics math.