ELi5: Why is it that if you are in a moving train and jump, you stay in the same spot, but if you stand on top of a moving train and jump, you do not?
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inside the train the air that surrounds you is also moving at the speed of the train. Outside the train the air is sitting relatively still, so whatever speed the train moves forward a simulated wind pushes force on you in the opposite direction causing your airborn body to slow down and maybe even veer off from the train beneath.
Internally jumping in the car has no acceleration(assuming a perfect vertical jump and no other forces). You are moving at 10m/s relative to the ground, the train is also moving at 10m/s relative to the ground being propelled by an engine with constant force, the air inside the train is moving at 10m/s relative to the ground. You jump, there are very little forces impacting you in the air inside a train car. You land in the same spot.
Outside of the train, the train is moving relative to the ground and being propelled by an engine at a constant force, you are moving relative to the ground, but the air is stationary.
Standing on the top of the train, your shoes impart a force(assuming you can even stand up there depending how fast the train is going) which keeps your velocity “linked”.
By jumping you unlink yourself from the train and now become an object that is flying through the air. There is no propulsion pushing you forward(as there is with the train engine), so effectively you are being acted on by all drag pushing back from the relatively stationary air(wouldn’t be truly stationary and would be disturbed from the passing train but that’s getting into the weeds of fluid dynamics).
Not entirely the same, but if you’re interested you should check out this video (and channel for that matter) which this question reminded me of.
Highly recommended
Air resistance.
Inside the train cabin, all the air is also moving along with the same forward speed that you and the train have. So even while you’re in the air, there’s nothing pushing sideways on you.
Outside of the train, the air is standing still. So when you’re on the roof of the train, you and the train are moving forward with the same speed, but the air isn’t. So when you jump, you’re moving at 50mph in stationary air. That’s the same as a 50mph wind pushing back on you, so you move back.
This is all the same reason why when you’re driving 80mph in a car you don’t feel a wind in your face. The air inside is going along with you.
The gaseous matter inside the train that surrounds you is also moving forward. The gaseous matter outside the train that surrounds you is flying past you / pushing you back.
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