In itself, this question is very interesting. During my teaching career, physics students and just acquaintances asked it, probably 50 times. However, if you do not specify under what conditions a person will jump into such a tunnel, it is impossible to answer this question.
In any case, we must neglect the enormous temperature of matter at the core of the Earth, because of which the tunnel will be destroyed and the experiment will definitely fail. Also, we will not take into account the fact that such a tunnel is physically impossible to drill.
Let's go back to the moment with the conditions of the experiment. The fate of our jumper depends on whether he is in a spacesuit or jumping in ordinary clothes? Does he have a durable capsule that will save you from incredible pressure or not? Is there air in the tunnel or is it evacuated to full vacuum? Let's go in order.
Let's imagine that a person jumps into this tunnel without a capsule and a spacesuit, in ordinary clothes. In this case, he will die, not even flying a quarter of the way. It's all about the pressure of the atmosphere, the deeper we plunge into the atmosphere, the denser it becomes and the more pressure it creates. Already at a depth of 100 km below the surface of the planet, the pressure is comparable to the pressure at the bottom of the Mariana Trench - the deepest point in the ocean. In other words, a person will simply be flattened by 1/60 of the way.
Now, suppose that all the air has magically disappeared from the tunnel and the pressure is no longer a hindrance to us. In this case, the person will simply be rubbed into powder against the walls of the tunnel and the reason for this will be the Coriolis force, which will press him against the wall of the tunnel. After all, the Earth rotates, and the speed of rotation of its surface is greater than the speed of the inner parts of the planet.
If you do not quite understand what I mean, then imagine a vinyl record in front of you. If you rotate it, then after making a full turn, the extreme point of the plate will go a longer way than the point located at the very center.
The Earth rotates in a similar way, its rotation speed on the surface is about 1600 km / h, and half way to the center - 800 km / h. Consequently, our jumper will have to extinguish the speed of 800 km / h, he can do this due to friction against the walls of the tunnel, which will erase him into dust.
The only situation in which there will be no Coriolis force and the jumper will not be pressed against the wall is if the tunnel is laid strictly along the axis of the Earth's rotation.
Summing up, we get that in order for the jumper to survive, ideal conditions for the experiment are needed: the tunnel must be isolated from the heat of the Earth's core and withstand colossal pressure, all the air must be pumped out of it, and it must run strictly along the axis of the Earth's rotation.
In this case, a person who has jumped inside will fly to the center of the Earth all the time, accelerating, after passing the center of the planet, he will begin to slow down until he reaches the other end of the tunnel, where he will stop for a moment and immediately set off on a new identical journey, unless no one else is. catches. The path itself between the ends of the tunnel will take about 42 minutes.