A competitor shoots a plate by using a rifle of 2,5 Kg on a skeet shooting competition. Knowing that the ball is 23 g and it is shot horizontally at 350 m/s, what is the recoil of the rifle?



mass of the rifle
  mr=2.5 kg
velocity before the shot 
vir=0 m/s
velocity of the rifle after the shot
vfr=? m/s
mass of the bullet
mb=23 · 10-3 = 0.023 kg
velocity of the bullet before the shot 
vib=0 m/s
velocity of the bullet after the shot
vfb=350 · i m/s


If we consider the bullet and the rifle as a system, the outer forces to it are cancel since, initially, both are held by the handle, therefore the conservation linear momentum principle, momentums before the shot (pi) and after the shot (pf) are the same:

pi = pf

For this reason  we are going to calculate the linear momentum of the system at that time, having into account the momentum of a system is equivalent to the sum of momentums of the bodies separatly:

Momentum before the shot pi = pib+ pir pi =mb·vib+mr·vir pi =23·10-3·0 +2.5 ·0  pi = 0 kg · m/s
Momentum after the shot pf = pfb+ pfr pf =mb·vfb+mr·vfr pf =23·10-3 ·350 ·i+2.5·vfr  pf = 8.05 · i + 2.5 ·vfr

Matching both linear momentums and solving for vfr, we can calculate the rifle´s  speed of recoil after the shot. 

0 = 8.05 · i + 2.5 ·vfr vfr =-8.052.5·i vfr =-3.22 · i

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Related sections
F=0 p= constantdpdt=0