physics course. Although we don't bother with the ladder. You just drill a hole all the way through the center of the earth, straight on through to the other side. Assume the entrance and exit holes are at the same distance from the center of the earth, or "elevation". Assume no air resistance.

Some interesting observations.

1) When you fall through, since there is no air resistance, you continue to gain velocity as you fall down the hole. The fastest you travel is at the very center. After passing the center, you "lose" velocity at the same rate that you gained it.

2) Your velocity turns to zero just as you exit the opposite side of the hole. You can just pop out the other side at precisely your own height, and then you fall again. Conceptually, your motion is nearly identical to being on a swing, or a simple harmonic motion.

3) What is fascinating is that the force of gravity gets weaker as you approach the center of the earth, where it is zero. You can calculate the force by integrating the gravitational force of all of the atoms in the earth. The math ends up causing the particles that are "higher" than you in elevation to cancel each other out. So in reality, the gravitational force is being generated by a smaller and smaller sphere whose radius is exactly your distance from the center of the earth.