Problem about jumping

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?

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) ignores: 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.

Bingo.

The simplest way to visualize it, is to replace all the air with water.

Inside the train is filled with water. If you swim upward a little bit (jumping) and float back down you will be in the same spot, as all the water is trapped inside the train and therefore not moving from your perspective.

Outside the train, the water is all rushing backwards (from your perspective on the roof of the train) so when you swim upward and float back down you will be further back, as you are carried by the water.

It is really that simple. Anytime you are having trouble visualizing something related to air, often if you replace it with water, it will make sense. Air is just water that weighs less.

The result point:

When moving with the train, the speed of the train is your speed. You are in the same frame of inertia. When you jump in the train, you do not encounter air resistance, and you usually encounter little to no force and there is no change in your speed. That’s why you fall in the same place when you jump. Because the speed of the train is the same as your speed. But when you do the same action outside of the train, you will encounter the resistance that the air exerts on you. This resistance exerts a force on you in the opposite direction of your movement. Because of this force, your speed decreases and the position when you jumped and the position you fell would not be the same. So the speed of the train and your speed are no longer the same.