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I'm sitting on my seat in a train and the train is moving at a very high speed, let's say 600 mph. If I throw a ball vertically up in the air (while still sitting on my seat), will the ball fall back in my hands or will it fall in the seat behind me since my position would have changed from the time I threw the ball, but the balls vertical trajectory will remain the same?

Qmechanic
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Sean Bernardino
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  • You've already done this experiment; the earth is moving even faster than 600 mph. – Brian Moths Dec 06 '13 at 21:12
  • This question does not appear to have anything to do with relativity. – Asad Saeeduddin Dec 06 '13 at 21:30
  • Related: http://physics.stackexchange.com/q/89098/ – joshphysics Dec 06 '13 at 21:32
  • @joshphysics The OP's question makes no mention of the train accelerating. – Asad Saeeduddin Dec 06 '13 at 21:37
  • @Asad This is just a limiting case of the accelerating train when $a\to 0$, so sure, it's no the same; it is related. I personally think it's extremely instructive to see how the accelerating solutions limit to the non-accelerating vertical solution (see my answer to the other question), and I think it will give the OP insight into his question as well. – joshphysics Dec 06 '13 at 21:42
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    Possible duplicates: http://physics.stackexchange.com/q/7479/2451 , http://physics.stackexchange.com/q/14993/2451 and links therein. – Qmechanic Dec 06 '13 at 21:54

2 Answers2

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Provided the train does not accelerate or decelerate during the ball's flight, it will fall back into your hands, since the ball is moving at the same velocity as you and the train.

Asad Saeeduddin
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As with any questions about (classical) motion, think about what forces are involved. Once you throw the ball in the air, what forces act on the ball? What forces act on you?

There's gravity, pointed vertically downward. There's some air resistance pointed in the opposite direction of motion (so down while the ball is going up, and up while the ball is going down). And that's it.

Now for you. You're in the chair, so there's some gravity down. And a chair normal force upwards to hold you still. What other forces act on your body? It depends on if the train is accelerating or not.

So -- all the forces on the ball are vertical. If you're not accelerating, all the forces on you are vertical. Hence the ball falls back into your hand. If you're accelerating, there's a horizontal force on you that isn't on the ball. So the ball moves horizontally relative to you (or in the frame of the ball, you move away from it because you're accelerating).

Always think about the forces. Always draw free-body diagrams.

tpg2114
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