Body Cushion

A fall from a height of several stories onto pavement or even onto a lawn will produce serious injuries or even death. Yet we have seen the movie hero going over the edge of a roof holding another human body in position just beneath to cushion the fall on impact. Certainly, collision with this second body is better than direct collision with the ground. What do you think about the advantages here?

Answer

We doubt whether landing on top of another body after such a long fall provides much cushion! The important parameter here is the extent of the collision time Δt that is, how long the collision of the hero’s body with the object actually lasts. The longer the Δt, the better. We also need to know the acceleration a versus time profile. In better words, what is the maximum acceleration to be experienced by the hero’s body? By definition, the average a = Δv/Δt, where Δv is the velocity change during the time interval Δt. Shorter Δt’s make the experience more painful.

Stunt professionals are often seen leaping off buildings or falling through windows in movies, but their collisions are with huge air-filled balloons that effectively extend the total collision time to half a second or more. We do not see their collision with the balloon in the program because the editing process substitutes the desired body lying dead on the concrete. Back to the hero landing on the other body. The collision time here will be less than one-tenth of a second, producing dangerous accelerations.

For example, if the body falls from the top of a two-story building, its speed will be approximately 11 m/sec just before collision. The acceleration during the collision will be greater than 110 m/s², very dangerous. Even if bones are not broken in bringing the hero’s body to rest, the internal organs will continue to move until they suffer a collision inside the hero’s body. And if the hero bounces back upward, the acceleration can be even worse, because the change in linear momentum will be almost double, even though the collision duration may be increased slightly. Automobile collisions provide plenty of evidence about the damages done to internal organs by sudden collisions with very short collision times. We doubt whether our hero will be able to walk away from the “body cushion.” In fact, our hero will be lucky to survive!