When the train is running, it usually travels at a constant speed. If they jump vertically, they will go back to their original place.

First of all, let's clarify the definition of inertia: we call the characteristic that an object keeps a constant state of motion inertia, or all objects always keep the original state of motion or static state when they are not acted by external forces. All objects have inertia. Specifically, you can encyclopedia.

Therefore, when people jump off the ground vertically, there is no external force in the horizontal direction. Therefore, in the horizontal direction, people should keep the original state of motion, that is, the state of moving at a constant speed like the train, so they will return to the original place when they land.

But strictly speaking, it will not completely fall into place, because there will be a little air resistance.

PS: The earth keeps turning. If there is no inertia, people can save a lot of money by jumping in place a few times.