Question

A 96.3 kg cannon at rest contains a 9.5 kg cannon ball. When fired, the cannon ball leaves the cannon with a speed of 84.58 m/s. What is the recoil speed of the cannon?

Answer 1

Using conservation of momentum:

`p1=p2`

Since the cannon is at rest before shots the ball:

`\begin{gathered} p1=0 \\ _{\text{ }}and \\ p2=mv+MV \end{gathered}`

Where:

`\begin{gathered} m=9.5kg \\ v=84.58(m)/(s) \\ M=96.3kg \end{gathered}`

So:

`0=9.5\cdot84.58+96.3V`

Solve for V:

`\begin{gathered} 96.3V=-9.5\cdot84.58 \\ 96.3V=-803.51 \\ V=-(803.51)/(96.3) \\ V\approx-8.34(m)/(s) \end{gathered}`

Answer:

The recoil speed of the cannon is approximately 8.34 m/s