Given,
The mass of the cannon, M=100 kg
The mass of the cannonball, m=7.50 kg
The velocity of the cannonball, v=15 m/s
From the law of conservation of momentum, the total momentum of a system remains constant at all times. Thus in order to give momentum to the cannonball, the cannon should acquire momentum equal in magnitude in the opposite direction.
Thus,
[tex]Mu=mv[/tex]Where u is the recoil velocity of the cannon.
On substituting the known values,
[tex]\begin{gathered} 100\times u=7.50\times15 \\ \Rightarrow u=\frac{7.50\times1.50}{100} \\ =1.125\text{ m/s} \end{gathered}[/tex]Thus the recoil velocity of the cannon is 1.125 m/s
