The Magical Shotgun (and it’s close cousin, The Magical Pistol) is a staple of the over-the-top action movie. The Magical Shotgun will be familiar to anyone who’ve ever watched a John Woo film: a character hit by a shotgun blast is thrown backwards at great speed through the air, usually into a plate glass window.
Unfortunately this just isn’t possible and the Law of the Conservation of Momentum explains why: in any collision, whether it’s a car striking a bus, or buckshot striking our leading man, momentum must be conserved. The total momentum before the collision must equal the total momentum after the collision.
Momentum is the product of mass and speed and can be loosely thought of as indicating how difficult it would be to change the motion of something. The graph below shows how momentum changes — a darker background indicates greater momentum.
The momentum before the collision is the mass of the shot multiplied by its speed: using typical values of 30 grams of shot travelling at 350 metres per second we have a momentum of 10.5 kgm/s. After the collision the momentum is the combined mass of the target plus the shot, multiplied by the speed of the target moving backwards.
If we assume the target is an average-sized man with a mass of 85 kg and that he’s standing still before he gets shot then the combined mass is 85.03 kg, which, with a momentum of 10.5 kgm/s gives us a final speed of 0.12 m/s or twelve centimetres per second (0.27 mph); this bears no relation to what’s seen on film.