Most shooting incidents in trailer and action movies portray a backward displacement of the victim (sometimes violent) over a large distance. Real life witnesses however may not give a similar account of the event. Viewers may also be skeptical on the way the incident is portrayed in movies. The effect of the bullet on the target can however be calculated from simple concepts in physics given the right or (reasonably approximated) quantities. The main concepts are those of momentum and energy conservation.
Firearms such as guns are meant to deliver destructive energy to the target with minimal energy input by the shooter. The momentum however by the shooter due to the shot cannot be different from that by the target (assuming the difference in the weight is negligible). In terms of physics the process involves a collision whereby the bullet is embedded in the body of the target. Such a collision is an inelastic collision. In this collision, the kinetic energy (given by the equations below) is not conserved.
Where KE is kinetic energy
M is mass of the object
v- Is the velocity of the object)
Rather the energy is destructively dissipated in the body of the target usually causing physical and physiological injury. The momentum however is conserved. The equation for the conservation of momentum is given by
m1U1+M2u2=m1+M2V
Where m1 is the small mass in this case the mass of the bullet,
M2 Is the mass of the target
U and u are the velocities of the bullet and target respectively before the collision
V is the final velocity of the body into which the bullet is embedded.
The mass of the targets body,
The velocity of the bullet and that of the target
Using the common firearm that is 44 Remington Magnum, the bullet has a mass of 14.58g and a velocity of 374m/s (according to impact guns website). we will assume the mass of the target to be 80Kg and his velocity before collision zero or at least negligible compared to that of the bullet. Further assumptions are going to be made in these calculations that the velocity of the bullet is not affected by the air resistance and the initial velocity is same as that hitting the target. Also the bullet hits the target normally or the motion after the collision is still linear. The velocity of both the bullet and the target is given as
-momentum before collision; m1U1+M2u2
Substituting the values
The value V can be given by m1U1+M2u2÷m1+M2
Substituting;
5.45292÷80.01458=0.06815
So V=0.06818Km/hr.
Converting to m/s gives
0.01911m/s
This value would be lower with greater mass of the target or greater with lesser mass. The difference is however not significant and a generalization can be drawn from the working above. Similar handguns would also give a generally similar solution e.g. Ruger Super Redhawk 44, Eagle 44 Magnum, Taurus model 44.
On average a pedestrian walks at 1-2m/s, the speed above id therefore negligible. The effect due to the momentum of the bullet therefore has no effect on the target; at least there cannot be an observable effect. There would however be a significant impact if the riffle was much bigger to the order of 20mm cannon shells. Such firearms are however not handheld or but mounted and not common in street fighting.
D=s×t
Where we have; D being the distance 1 meter
S is the speed 0.1911m/s
T is the time to be determined.
Substituting
1=0.01911×t
T=52.6315s
This time taken for such a displacement is not rational or is at least not what is observed.
There is also the dynamics associated with the kinetic energy of the bullet. The kinetic energy would be given by:
KE=12mv2
Substituting;
0.5×0.01458×3742=1119.69J.
In the above calculations air resistance is also neglected and the velocity of the bullet is assumed to remain constant.
Given its small size and high velocity, the bullet would exert high internal stresses in the target. This results in the penetration of the bullet in to the body of the target. More energy is lost in the passage of the bullet. The kinetic energy of the bullet is therefore almost wholly absorbed upon the collision with the target.
The workings above therefore illustrate explicitly that the dynamics involved in momentum and kinetic energy are not sufficient to account to the rather exaggerated distances or and speed of the reaction of victims to gunshots. We cannot however dismiss the moves as camera tricks as there could be other consideration. During the point of impact, there is imbalance caused by the gunshot usually causing the victim to fall. In bid to maintain counter balance, especially for skilled fighters, subconscious neuropsychological reflexes may come into play. These may cause the victim to try making some backwards move. This is not however a phenomenon as common as to appear in all shooting scenes.
References
Walker, J. S. (2004). Physics (2nd ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.
Asimov, I. (1966). Understanding physics. New York: Walker.
Cutnell, J. D., & Johnson, K. W. (1998). Physics (4th ed.). New York: Wiley.
Halliday, D., Resnick, R., & Walker, J. (1993). Fundamentals of physics (4th ed.). New York: Wiley.
Gibilisco, S. (2002). Physics demystified. New York: McGraw-Hill.
Ohanian, H. C. (1985). Physics. New York: Norton.
Walker, J. S. (2004). Physics (2nd ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.
