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Let's assume that the plane turns hard, like a fighter jet. The ball would seem to move in mid-air as the plane turned. if you were strapped into the plane, you'd turn with it and see the ball move sideways. If you were just standing unsupported, you would move sideways with the ball for an instant and then probably fall over.

If the airplane is in coordinated flight (the relative airflow meets the airplane head-on) then the ball acts as the airplane is level, but apparent gravity (G) increases in proportion to both angle of bank and indicated airspeed.

An observer on the plane will see the ball curve with the curvature more or less based upon how quickly the plane is turning.

Now lets look at it from someone in a plane flying parallel to the original plane that doesn't turn (and we'll assume the plane with the ball is transparent). An observer on the second plane will see the ball follow almost the identical path as the ball without the turning plane. The path will not be exactly the same because the air is moving with the plane and it will exert a force on the ball in mid-flight, but this force isn't terribly strong--which is why you can throw the ball through the air in the first place.

Imagine you and your furry friends are playing fetch inside a huge, enclosed dog park that can move, like a giant, mobile playpen. While you're playing, the dog park starts to turn.

When you throw the ball in midair, and the dog park turns, the ball appears to move along with the dog park. This is because the ball, you, your furry friends, and the dog park are all part of the same moving system. It's like when you're running with a toy in your mouth – the toy moves with you because it's part of your system.

In the case of the airplane, the same thing happens. When the airplane turns, the air inside moves along with the airplane. Since the ball is surrounded by the moving air, it also moves along with the airplane. To you and your friends inside, it seems like the ball is following a straight path, even though the airplane is turning.

So, if you were inside a big enough airplane and threw a ball while the airplane turned, the ball would appear to continue moving in a straight line, just like it would in a stationary dog park.

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This one is pretty trivial. The result will be the same be it plane, train or a boat.

A little bit trickier puzzle: What would happen if I had a big enough airplane to fly a small helicopter or a drone inside. Will the plane become lighter?

That's an intelligent five year old!

Only changes in speed or direction would be noticeable.

Think about that fly buzzing around in the car while we’re driving. Flies can’t fly 60mph, right? He flies normally because inside of the the car, he is part of the car. But, if we slammed on the breaks really really hard, the fly would move towards the windshield, and so would you. That is why we have seatbelts :)

I one time tried to jump really really high, so high that the Earth would keep spinning under me and I would land in a different place. But I landed in the same spot. Better idea, I tried to throw a rock super high. But it came straight down too.

It turns out the earth is our car and we are like the flies!

This is untrue. During a coordinated turn, all forces balance such that apparent force of gravity acts straight down as seen from inside an airplane with no windows. The rolling motion that sets the bank angle needed to turn can be felt. But once established in the turn, without windows or instruments, it is impossible to deduce that the airplane is turning in a particular direction.

While sitting in your seat during a turn, if you threw a ball straight up, It would come straight down again. The only discernable change is the apparent strength of gravity.

Here is a great demonstration of the primciple. The pilot performs a barrel roll, which is like a turn, except roll continuously increases in a particular direction until the airplane is upright again. Again, like a turn, once the forces needed to establish the barrel roll are complete, apparent gravity acts vertically through the airplane, pulling the water into the cup.

Check out Mythbusters. They did a show with pigeons and a model helicopter in a truck to test whether the truck became lighter when things inside the truck were in flight.

They tested the pigeons and the helicopter separately otherwise things might have got a bit messy.

Imma say no.

Helicopter works by pushing air down. That air hits the floor of the plane, giving the same "weight" as the helicopter just sitting there anyway.

A real interesting question is what happens if I have a big train going half the speed of light. Then stick another train on top going half the speed of light. Does the second train go at the speed of light?

They specifically said "if it turns hard, like a fighter jet" while the ball is "in mid air"

I know the answer. I just thought it is a bit more fun question.

But apparently some people here struggle even with the OP's original question from middle school. Newton's first law. Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

Sure it won't.

As with speed of light the answer is also no even if you put a third train on top of the second. But I fear I am not able to eli5 this.

You're right it won't. The short answer is that adding velocity together is an approximation that only works for low speeds. It doesn't work when you get near the speed of light.

This link explains better than I can https://galileo.phys.virginia.edu/classes/252/adding_vels.html

Yes. From their "strapped in seat" the passenger will see the ball fall directly to the cabin floor, just with a lot more force than in level flight. From the passenger's perspective the ball will not move sideways.

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