Using conservation of momentum:
[tex]p1=p2[/tex]Since the cannon is at rest before shots the ball:
[tex]\begin{gathered} p1=0 \\ _{\text{ }}and \\ p2=mv+MV \end{gathered}[/tex]Where:
[tex]\begin{gathered} m=9.5kg \\ v=84.58\frac{m}{s} \\ M=96.3kg \end{gathered}[/tex]So:
[tex]0=9.5\cdot84.58+96.3V[/tex]Solve for V:
[tex]\begin{gathered} 96.3V=-9.5\cdot84.58 \\ 96.3V=-803.51 \\ V=-\frac{803.51}{96.3} \\ V\approx-8.34\frac{m}{s} \end{gathered}[/tex]Answer:
The recoil speed of the cannon is approximately 8.34 m/s
