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Please ignore all relativity stuff.

Consider two cases.

Case 1: Train moving at constant speed.

Case 2: Train with constant acceleration.

I'm standing on the ground with a ball in my hand. I throw it towards a moving train door.

I know everything inside the train should travel at train speed.

Now, when I throw the ball I know it has certain velocity traveling away from me.

When the ball enters the train door will it acquire the velocity of the moving train in the direction of train?

Will the ball pass through the other door?

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  • $\begingroup$ "When the ball enters the train door will it acquire the velocity of the moving train in the direction of train?" . Not unless it becomes attached to something on the train. $\endgroup$
    – Bob D
    Nov 9, 2021 at 14:20

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When the ball enters the train door will it acquire the velocity of the moving train in the direction of train?

No. To change the horizontal velocity of the ball there would have to be a force acting on it with a horizontal component, and there is no such force. Even if we include air resistance, the effect would only be significant if we had a very light ball.

Will the ball pass through the other door?

That depends on many factors - the speed and direction of the ball, the speed of the train, the width of the train, the width of the doors etc. Working in the reference frame of the train, you would have to subtract the train’s velocity vector from the ball’s velocity vector and see if the ball could now go from one door to the opposite door. If the ball is travelling much faster than the train (if you hit a baseball through the train, for example) then this is certainly possible.

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