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Imagine I would be on a mobile belt-conveyor and throw a ball in the air, then the ball would not fall in my hand, because I move to the right but the ball does not, just like this:

enter image description here

However, if I would be in a wood-box and throw a ball up, it would go up and down in a straight line and land in my hand, while the box moves the the right:

![enter image description here

Why is it like that? I would expect that the ball would not land in my hand. How come the ball also moves to the right in the box?

Adam
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  • Have you tried this yourself? As in, walk down the sidewalk, throw a ball straight up while walking and see where it lands? – noah Mar 23 '21 at 14:45
  • @noah I would like to but I don't have a box and a mobile belt-conveyor where I could try it. My question is about the image with the box, maybe its better if I switch the images for clearity – Adam Mar 23 '21 at 14:48
  • You don't need a conveyer belt, just keep walking while throwing the ball to see if your assumption about the second case is correct. – noah Mar 23 '21 at 14:50
  • @noah so I edited the sequence of images. Hope its more clear now. If I throw a ball in the air and move, of course the ball will land behind me. No need to test that? – Adam Mar 23 '21 at 14:52
  • Wait, are you stationary, throw the ball, then only then move to the right? – noah Mar 23 '21 at 14:54
  • @noah my question is about the (now) second image, where I don't move and stand inside a box that moves to the right. I wonder why the ball will "move with me and the box", although I throw it up – Adam Mar 23 '21 at 14:57
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    You seem to be asking why, if you are on a conveyer belt inside a box, does the ball land in your hand, but not without the box. I am questionig your assumption that it will not happen like this without the box. If you actually tried this you might have an aha moment. – noah Mar 23 '21 at 15:00
  • @noah okay if I throw the ball when I am stationary and move then, the ball lands behind me. If I throw him while I am moving, he lands on my shoulder. If the above example is too complex, maybe its better to think of the ball just as a bird that is on top of me (without moving, just keeping it up beeing in the air). On the conveyor I would move away from the bird, but in the box, the bird would move with the box. My question is now, why? – Adam Mar 23 '21 at 15:06
  • Why would it land on your shoulder? – noah Mar 23 '21 at 15:11

3 Answers3

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Ideally, in both cases the ball will land in your hand. In both cases the thrown ball will move along with you.

  • The first case is non-ideal, though, since you might have sideways air resistance slowing down the ball. You yourself are not being slowed down since the conveyor belt forces you forwards and overcomes air resistance. So, although the ball will move forwards as well, it will not move as fast forwards as you and will be lacking slightly behind.
  • In the second case, all air inside the box already moves along with you at the same pace. So there will be no sideways air resistance when you throw the ball.

So these examples are not really about velocity vectors "adding up" (or syncronising) inside a box, but rather about velocity not being affected when there are no forces to affect it. If you inside the box blew with compressed air sideways on the ball, the ball would naturally also be pushed away and will not land in your hand inside the box either.

Steeven
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Air resistance matters. If you performed the experiment in a vacuum, both the first and second cases would end with the ball landing in your hand. But in Earth's atmosphere the moving belt conveyor creates a wind (from your perspective) which pushes the ball away from its natural trajectory. The effect of the wind depends on the relative velocity of the conveyor through the air -- at low speeds you probably wouldn't notice it (the ball would fall in your hand). In the box case the box would shield you from the wind.

Eric Smith
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To answer your question directly; all vectors "add up", meaning we can decompose all dynamics into a sum of dynamics in different directions; the most basic of which being 2D motion decomposed into x-direction motion plus y-direction motion.

Here in the y-direction our equation of motion would be some initial velocity upwards, with constant acceleration down (gravity); you can use this to calculate the y-direction kinematics of the object.

Now in the x-direction, our equation of motion would be the initial velocity which we had on the conveyor belt (which the ball also had), and there is no net force in the x direction, so the acceleration is 0. Therefore it maintains the conveyer belt velocity in the air.

So the height of the object is changing with constant acceleration, but while this acceleration is happening its x-velocity, is the same as ours on the conveyer belt, as a result it will alway have the same x-coordinate as us moving on the conveyor belt, and inevitably when it falls back to our y-level, it will still have the same x-coordinate as us, and land in our hand.

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