Final answer:
Yes, it is possible for a hat to come off the head of an elevator passenger when the elevator rapidly stops during an upward ride, without the person being tied to the floor of the elevator.
Step-by-step explanation:
Yes, it is possible for a hat to come off the head of an elevator passenger when the elevator rapidly stops during an upward ride, without the person being tied to the floor of the elevator. This is because of the principle of inertia. When the elevator suddenly stops, the person's body tends to keep moving forward due to its inertia, but the hat, being an object not directly attached to the person's body, tends to stay in place. As a result, the hat may fly off the person's head.