Final answer:
Yes, a hat can come off a person's head in an elevator that stops abruptly due to inertia, where the hat continues moving by momentum until another force acts upon it, such as gravity pulling it down.
Step-by-step explanation:
The question as to whether the hat coming off the head of an elevator passenger when the elevator rapidly stops during an upward ride is based on physics principles, specifically Newton's laws of motion. Yes, this could really happen due to inertia. When the elevator suddenly stops, the passenger's body and anything not secured to it, like a hat, will continue moving upward due to inertia until acted upon by another force. If the hat is loosely sitting on the passenger's head, it may continue moving upward when the elevator stops abruptly, while gravity eventually pulls it down.
This effect is similar to how passengers in a car lurch forward when the car stops quickly. The same principles apply; the person and the hat have inertia and will continue in motion unless restrained. Therefore, there is no need for the person to be 'tied to the floor' of the elevator for the hat to come off.