Final answer:
Catching a falling person a hairsbreadth from the ground can be fatal due to a concept called impulse, where a sudden change in momentum can cause significant injury or death. The force exerted during the catch itself may also result in injury.
Step-by-step explanation:
The reason why catching a falling person a hairsbreadth from the ground can be fatal is due to a concept called impulse. Impulse is the change in momentum of an object, which depends on both the magnitude and duration of the force applied to it. When a person falls, they accelerate due to the force of gravity, and when they reach the ground, they experience a sudden change in momentum as they come to a stop.
If a superhero catches the falling person just before they hit the ground, they must exert a force to bring the person to a stop over a very short period of time. This high force over a short period of time can cause significant injury or even death to the person being caught. It is similar to the impact force that would occur if the person hit the ground directly.
Additionally, the catch itself may also result in injury. The person's body may not be prepared to absorb the sudden force or change in direction, which can lead to fractures or internal injuries.