Why does a sheet of paper on top of a large book fall and land at the same time as the book?
By itself, a falling sheet of paper experiences severe air resistance as it moves downward through stationary air. It soon reaches a small terminal velocity — the downward speed at which the upward force of air resistance cancels its downward weight and it stops accelerating downward. The falling book protects the sheet from that air resistance, so the sheet can fall unimpeded.
All objects that move downward through stationary air experience upward air resistance forces, but heavy compact objects (e.g., books) are less affected by those forces than light, fluffy ones (e.g., sheets of paper). Although a book falls mostly unimpeded through stationary air, it does affect the air it encounters. Most importantly, it drags a pocket of air with it. The air just above the book is moving downward at approximately the book’s velocity. When a sheet of paper is located in this special region of downward-moving air, it can fall with the book and experience virtually no forces due to the air.
This behavior is known as drafting and is important in many types of races, including running, bicycling, skating, and swimming. For example, a bicyclist drags a pocket of air with her and a second bicyclist following close behind her and located in that pocket of forward-moving air experiences less air resistance. Consequently, a group of bicyclists traveling in a tight line makes easier forward progress through stationary air than separated bicyclists each fighting air resistance in their own. The lead bicyclist in the line gets the air moving for the others and exhausts first, so they typically take turns as the lead bicyclist. Some races forbid drafting because it provides such an advantage for the following bicyclist.
Drafting while skydiving is actually dangerous and is normally avoided. A descending skydiver creates a pocket of downward-moving air above them and when a second skydiver enters that pocket of downward-moving air, the upward air resistance decreases dramatically. The second skydiver suddenly accelerates downward due to weight and can drop onto the first skydiver. This is usually a bad idea and can lead to disaster. Similarly, the sheet of paper drops onto the book below it, but the only possibility of injury is if they land on your foot.