ANSWER:
273566.08 m/s²
27914.90 g
STEP-BY-STEP EXPLANATION:
Given:
length of the canon (d) = 220 m
Final speed of the canon (v) = 10.97 km/s = 10970 m/s
Initial velocity (u) = 0 m/s
Average velocity inside the canon:
[tex]\begin{gathered} V=\frac{(u+v)}{2} \\ \\ \text{ we replacing:} \\ \\ V=\frac{0+10970}{2} \\ \\ V=5485\text{ m/s} \end{gathered}[/tex]With this velocity we can determine the time, like this:
[tex]\begin{gathered} V=\frac{d}{t} \\ \\ t=\frac{d}{V} \\ \\ \text{ we replacing:} \\ \\ t=\frac{220}{5485}=0.0401\text{ s} \end{gathered}[/tex]Finally, we calculate the acceleration:
[tex]\begin{gathered} a=\frac{v}{t} \\ \\ \text{ We replacing:} \\ \\ a=\frac{10970}{0.0401}=273566.08\text{ m/s}^2 \end{gathered}[/tex]To get in terms of dividing the acceleration by g = 9.8 m/s², we get
[tex]\begin{gathered} \frac{a}{g}=\frac{273566.08}{9.8} \\ \\ a=27914.9\text{ }g \end{gathered}[/tex]