ANSWER
[tex]-0.56m\/s[/tex]EXPLANATION
To find the recoil velocity of the gun, we have to apply the principle of conservation of momentum:
[tex]mu+MU=mv+MV[/tex]Since the total momentum of the system (gun and bullet) is conserved and 0 before the bullet is fired, the equation changes as follows:
[tex]0=mv+MV[/tex]where m = mass of bullet = 4 g = 0.004 kg
M = mass of gun = 4.50 kg
v = velocity of bullet = 625 m/s
V = velocity of gun (recoil velocity)
Therefore, substituting the given values into the equation and solving for V:
[tex]\begin{gathered} 0=(0.004\cdot625)+(4.5\cdot V) \\ \Rightarrow-4.5V=2.5 \\ \Rightarrow V=\frac{2.5}{-4.5} \\ V=-0.56m\/s \end{gathered}[/tex]The negative
