ELI5, why if you jump inside a moving train you will land on the same spot, but if you jump on the roof of a moving train, you land on a different spot?

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seen it on twitter and I can’t get my head around it
EDIT: thanks guys I get it now 😅

In: Physics
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In most cases you’ll see in high school physics, both should give the same result. But there is a big factor that high school physics (and depending on your field, uni physics) igbores: air. When you jump inside a train, the air inside it is moving along with the train as well. But the air outside of the train is still with respect to the ground, or moving with the speed of the train, in the opposite direction, with respsect to the train. The air then pushes against you, and when you jump, it blows you back. Of course this depends on how fast the train is going, and how strong the wind blows (and in what direction), but in general, that’s what happens.

Inside the train the air is not moving relative to you. Outside the train it is so it will blow you back. Like when you stick your hand outside a car window.

When you stand on the roof of a train, the train is pushing you forward (through your feet), and the wind is pushing you back (air resistance). As soon as you jump, you no longer have the train pushing you forward, but the wind is still pushing you back, so you move backwards.

When you’re in the train, you don’t have the wind pushing you backwards, so when you jump, you keep moving forward at the same speed as the train.

If you were on the roof of a train in a vacuum, and you jumped, you would land on the same spot, because again, there would be no wind pushing you back.

It’s basically Newton’s First Law of motion. If you’re moving, you keep moving until an external force stops you.

2 things here to consider: air resistance and velocity of the air relative to the train.

In the train, the air moves with the same velocity as the train, so no air resistance. This means, if you jump, you land on the same spot.

On the roof, the air does not move with the train, so there is a relative velocity in the opposite direction of the moving train. so if you jump, air resistance will cause you to be moved, so you land more to the back of the train.

Everything inside the train is moving with the train, *including the air inside*. When you’re on the roof, you’re moving with the train but the outside air is still stationary. When you jump, you keep your forward momentum, as you would if you were on the train, but this time your body is trying to move forward through stationary air, which slows it down.

Imagine a parachute. It slows you down by catching air. Same thing happens when you jump up on a moving train. You’re catching air which slows you down.

It doesn’t happen on the inside because the air on the inside of the train is moving with you.

Air resistance.

In both cases, before you jump you are travelling at the same speed as the train.

If you jump inside the train then all the air on the train is also travelling at the same speed as the train so it doesn’t slow you down.

If you jump on the roof of the train, the air is not moving at the same speed as the train so it effectively pushes you in the direction opposite to the train’s travel.

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Everything inside the train is moving at the speed of the train. This is not the case outside of the train. Outside the train, the train is moving faster then the air surrounding the train. So, essentially you are pushed back by the air surrounding the train.

TLDR – the air surrounding the train pushes you back if you are outside the train.

If you are moving with constant speed, you technically should land on the same spot but if you are on the roof, there´s a lot of air resistance and that will slow you down so it would be like you landed behind from the spot you jumped

Momentum.

Inside, you are moving the same speed as the train and so is the air inside. Outside, you are moving the same speed as the train, but when you separate from the train by jumping, you are transferring momentum to the air particles you are bumping into.

When you’re inside the train, basically everything is moving at the same speed (all things being equal).

When you’re outside, there are outside factors that will change where you land – air resistance, wind from any direction, etc.

If you jump outside on a still day you land on the same spot.
If its a day with 160kph winds you’ll land a bit downwind

Air resistance

The air inside the train is being dragged along with the train because the train carriages are enclosed boxes.
If you jump, the air moves with the same speed as you, and doesn’t drag you back.

The air outside the train doesn’t get dragged along with the train, and is usually stationary relative to the ground.
As you jump, you’re moving at the speed of the train through the stationary air, and the air pushes against you a little, slowing you down and meaning you land a little closer to the back of the train

Ideally, both scenarios will result in you landing on the same spot. This is due the fact that when you jump, you are still moving at the same speed as the train. The difference when you’re on top of the train is that air resistance will drag you down and you’ll land short.

I would say speed and distance.
Typically a moving train that you’re jumping into, is still going very slowly (otherwise I wish you good luck…..). And also the distance you’re jumping is very small. You’re jumping only a few feet horizontally, after you matched your speed to the slowly moving train. So yeah, as long as you match the speed you will land kinda where you were aiming. Kinda, because typically the train will be accelerating (slowly) and you can’t accelerate mid air. 😋

Whereas people jumping on to trains in movies (don’t try it at home) typically jump onto a train moving at moderate to fast speed. So they are unable to match the forward momentum of the train. AND they are jumping maybe 10 to 20 feet vertically from a bridge. More like “aimed falling” than jumping. 😅 And during falling, simple gravity acceleration rules will apply. During that second or two that falling 10 to 20 feet will take, the train will be moving under you.

From km/h to m/s, you need to divide by 3.6.
So let’s say the train is moving at a modest speed of 36km/h to keep it easy. That’s 10 meters that the train will have moved forward if let’s say you are falling for 1 second. Sure, you too will have moved forward some if you took a running start before jumping off the bridge. But surely not 10 meters.

We land on the same spot, when we jump inside, because you’re moving along with the moving train! (YOU HOP UP INTO IT, HAVING THE HANDLE IN YOUR HAND….YOU’RE MOVING WITH IT!)

Whereas, when you jump on the roof(say, from a chopper)….it drops you down, where you leave it( means: it leaves you at the foot of the perpendicular from the position of the chopper((when you left)) ) while the train is still moving!

This is why it happens!