Gunfight

Some TV programs and films have high drama scenes based on a victim being shot by the pursuer and being “blown backward” a meter or two by the projectile impact. Is this dramatic response Hollywood hype, or is there good physics here?

Answer

One could do good classical physics here, but the filmmakers have turned the scene into Hollywood exaggeration. The physics is determined by the conservation of linear momentum. Assume that the victim of the shooting is initially at rest, so the total momentum initially is all in the bullet (or buckshot) of mass m and speed V before hitting the victim, at mV. After the collision, the final total momentum is in the backward “flying” person plus bullet. If the victim has mass M and the combined victim-plus-bullet object has speed v, the total final momentum is (M + m)v. For all interactions, by the law of conservation of linear momentum, the final momentum equals the initial momentum.

In the simplest case (assuming no frictional drag at the feet and ignoring transfer of momentum away to the earth, etc.), its application yields (M + m)v = mV. Solving for the velocity v of the victim afterward produces v = mV/(M + m). Substituting reasonable values of M = 80 kg, V = 400 m/s, and m = 0.03 kg yields a “blow-back” velocity maximum of v = 0.15 m/s. Most people can walk about 2 m/s (i.e., about 4 mph). So we can conclude that any shooting victim depicted as being blown backward by the impact of the bullet (or shotgun blast of pellets) is ridiculous and belongs in the fantasy world only!

A physicist wouldn’t actually need to calculate the velocity backward using linear momentum conservation explicitly. Simply watching the behavior and movement of the shooter holding the gun before and after the shot reveals approximately how much momentum is available by using Newton’s third law. If the shooter isn’t blown backwards by the recoil force of the shot, the victim won’t be either. Of course, someone will suggest that involuntary muscle contraction in the stunned victim causes the “flying” backward. Falling backward, perhaps,  but not “flying”!

There is the story of a famous physicist back in the 1950s who loved to watch gunfights in Western movies. The bad guy always draws first, he noticed, but the good guy wins the gunfight. How could this outcome happen? His hypothesis was that psychology played an important role, slightly hindering the man who had to make the conscious decision to draw first. The second man simply had to react. Even today, the psychology of choosing a physical action is an important factor, particularly in sports.

There are tennis coaches (and coaches in other sports) who preach the psychology of playing tennis, saying that when you think too much on the court instead of simply reacting, as you learn to do in practice, then you are in trouble. You are letting self no. 1 (your mind) control self no. 2 (your body), and your tennis game will suffer. We wonder whether the concepts hold true for playing the physics game, too!