24 Hour Hovering Helicopter

Although the first post defines the word hover, the physics behind the question still yields the same answer; the position of the helicopter will be unchanged with respect to the Earth's position where it was hovering.

Even though the Earth rotates, the helicopter is also rotating (or more correctly, orbiting) about the Earth's axis in tandem with the Earth. The same thing applies with a balloon in the air.

You can do a little thought experiment to prove it. The Earth is rotating once every 24 hours. The circumference is about 25,000 miles. That means the surface radial velocity is about 1,000 miles per hour (rounding down).

Now if you jumped into the air or off a diving board and were airborne for 1 second, at 1000 mph you would expect the Earth to move under you 1,467 feet in that 1 second.

Obviously, if you dove off a diving board you would miss the pool completely!

The math for my example is 1,000 miles per hour / 60 minutes = miles per minute.

Divide again by 60 seconds and you get miles per second, which is .278 miles.

There are 5280 feet per mile, so multiply 5280 by .278 and you get 1467 feet.

Now, which one of Newton's Laws does this illustrate?

If the helicopter was already halfway around the Earth from you when when it began its hover, yes, it would be halfway around the Earth from you when it lands.

In general, Sapper's response says everything that needs to be said.