Hollywood bullets

Often in films, a person hit by a bullet flies backward as though he has been hit by a bus. This has always struck me as a bit implausible considering the small mass of a bullet. So I decided to do some calculations to see if it really would happen like that.

The following numbers are based on data from the CounterStrike Firearms Directory. The 1947 Kalashnikov 7.62mm automatic rifle (AK47) fires a bullet of mass around 8 grams with a muzzle velocity of around 700 metres per second. This gives it a momentum of about 5.6 kilogram metres per second. If this bullet impacts on a human body weighing 70 kilograms, and gives up all its momentum to that body, it will change that body's velocity by about 0.08 metres per second, or 8 centimetres per second.

This means that a stationary 70 kilogram target, hit and instantly killed by a single bullet from an AK47 travelling at its full muzzle velocity which gives up all its momentum to the target, will start to move at a speed of 8 centimetres per second. This is a slow crawl. A body moving at 8 centimetres per second does not fly backwards. Rather, it would simply slump to the ground.

Even if the target was hit by a spray of 5 bullets, its velocity would change by only 40 centimetres per second, which is a slow walking pace. The body might fall over backward but it would not fly.

All the above rests on the bullet giving up 100% of its mementum to the target. My understanding is that solid hard-nosed bullets generally penetrate the target, coming out the other side having lost only a fraction of their momentum. I recall hearing that a rifle bullet can penetrate up to seven or so people before coming to a stop. This implies that it does not lose more than 30% of its momentum on each target (a bullet penetrating six bodies and losing 30% of its current momentum each time would have around 10% of its original momentum when leaving the sixth body).

If this is so, then the numbers above should be reduced by a factor of at least 3. Then, clearly, the motion imparted to the target by the bullet is negligible. People should not fly backward when shot.