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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?

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Is your train accelerating? You just said "fast moving". A correct answer to your question requires more specificity. –  D. W. Jul 14 at 15:44
    
It is moving at a constant speed. –  Jay Jul 14 at 15:50

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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.

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Thanks for the lucid explanation. –  Jay Jul 14 at 15:53

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