In the cabin of a jetliner that cruises at 600 km/h, a pillow drops from an overhead rack into your lap below. Since the jetliner is moving so fastm why doesnt the pillow slam into the rear of the compartment when it drops? What is the horizontal speed of the pillow realitive to the ground? Realitive to you inside the jetliner?

Is that why the air stewardess' always bring the pillows from the back? :)

The pillow is moving at the same speed as you when it drops. See Newtons first law.

The pillow does not slam into the rear of the compartment because, once it detaches from the overhead rack, it continues to move with the same horizontal speed as the airplane itself. This is because, inside the airplane, all objects, including the passengers, are already moving at the same speed as the airplane.

Relative to the ground, the horizontal speed of the pillow is also 600 km/h. This is because, when an object is dropped inside a moving vehicle (like an airplane), its horizontal speed remains the same as the vehicle, unless acted upon by external forces, such as air resistance.

Relative to you inside the jetliner, the horizontal speed of the pillow is essentially zero. This is because, from your perspective inside the airplane, the pillow appears to be moving at the same speed as you are. So, even though the airplane is moving at 600 km/h, the pillow appears to drop straight down into your lap without any horizontal motion.