In the cabin of a jetliner that travels at 600 km/h, a pillow drops from an overhead rack into your lap below. Since the jetliner is moving so fast, why doesn't the pillow slam into the rear compartment of the plane? What is the horizontal speed of the pillow relative to the ground? Relative to the inside of the jet?

The reason why the pillow doesn't slam into the rear compartment of the plane is due to the principle of inertia. Inertia states that an object at rest or in motion will continue to stay in that state unless acted upon by an external force.

When the pillow drops from the overhead rack, it already has the same horizontal velocity as the jetliner, which is 600 km/h. Since there is no horizontal force acting on the pillow, it will continue to move horizontally at the same speed as the jetliner.

Therefore, from the perspective of an observer on the ground, the horizontal speed of the pillow relative to the ground would also be 600 km/h. This is because both the jetliner and the pillow are moving together at the same speed.

Now, let's consider the relative speed of the pillow inside the jetliner. From the perspective of a passenger inside the jetliner, the pillow appears to be at rest relative to them. This is because both the passenger and the pillow have the same horizontal velocity due to being in the same moving frame of reference.

In summary:
- The pillow does not slam into the rear compartment of the plane because it has the same initial horizontal velocity as the jetliner and continues to move with that speed due to inertia.
- The horizontal speed of the pillow relative to the ground is 600 km/h, matching the speed of the jetliner.
- The horizontal speed of the pillow relative to the inside of the jetliner (from the perspective of a passenger) would be perceived as zero, as both the passenger and the pillow have the same initial horizontal velocity.