If I drop a ball in a train moving at a constant speed, will it land on the spot I aimed it at or a little away as the train has moved while it was in air? If it lands away, will the observer not know that he is in a moving frame of reference? If it lands on the intended spot, how did the ball know it is inside a train?
Assuming the train doesn't accelerate during the ball's fall, it will land in the spot you aimed at. Think about it this way. Before you drop the ball, it is moving along with the train (i.e. it has some horizontal speed). When you drop it, the ball still has this speed, and since an object in motion tends to stay in motion unless you exert a force on it (Newton's first law), the ball will continue to move at this horizontal speed as it falls. Thus it will land exactly where it would if the train were at rest and so the observer won't be able to figure out he is in a moving reference frame.
This actually speaks to something much deeper: namely that physics behaves the same in any inertial reference frame (a reference frame moving with constant velocity). There is thus no concept of "absolute motion." The train is moving with respect to the earth, but that is no different from the train being at rest and the earth moving underneath it.
Of course this all assumes that the train doesn't accelerate during the ball's fall. If the train accelerates, then the ball will still move as it would have if the train had not accelerated. Thus in this case the ball may land elsewhere than where you aimed it, and an observer can figure out in this case that the train is accelerating.
I have no real qualifications in answering this but there are several bits at play here. The basics are indeed that you are moving along with the train and if there is no acceleration or deceleration then everything in the train not attached to the train is still moving at the exact same speed as the train. So if you drop a ball, it will already have the same speed as the train. The next question is, shouldn’t the ball slow down separate from the train as long as it is not attached to the train. Here I think several other things come into play, one of which becomes obvious when you throw the ball out of the window. Obviously then the ball will very quickly have a different speed from throwing it inside the train, and that is because the air is not moving at the same speed outside the train. Gravity could in theory slow a free floating object in a train differently from the train depending on their weight that always has an engine keeping it moving (which costs a lot of energy where at increasing speeds air resistance becomes an ever increasing limiting factor) depending on the weight of the object, but something that is very light would be affected by the equally moving air more so that you wouldn’t see a difference, and something really heavy might show a bigger difference but fall so fast that you wouldn’t be able to notice a big difference either.
Intuitively I would also say that at sufficiently high speeds centrifugal forces would start to negate the power of gravity, but the earth is so big that will probably never be a very relevant factor. Someone with actual knowledge could probably calculate when.
In the end it is all about thinking about what does and does not impact the velocity of an object, and how much.
The ball will fall where you aimed it even if the train travel at maximum speed.you can try an experiment for it to see for yourself.why.....?because every space in the universe has a fabric. As long as there is no outside force such as air that affect the object, the object that suspended in the air will still move forward same as fast as the moving train with respect to the earth but the ball suspended in the air does not move even with a moving train with respect to the train.If its 3 meter away suspended in the air from the driver set,it is still 3meters away from the driver set even with a fastest moving train.Try to fly a drone inside a moving train, as long as the windows is close, the drone will fly where you want it to fly....