Question

In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.)_____ m/s2Compare your answer with the free-fall acceleration, 9.80 m/s2._____ g

Answer 1

273566.08 m/s²

27914.90 g

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:

`\begin{gathered} V=((u+v))/(2) \\ \\ \text{ we replacing:} \\ \\ V=(0+10970)/(2) \\ \\ V=5485\text{ m/s} \end{gathered}`

With this velocity we can determine the time, like this:

`\begin{gathered} V=(d)/(t) \\ \\ t=(d)/(V) \\ \\ \text{ we replacing:} \\ \\ t=(220)/(5485)=0.0401\text{ s} \end{gathered}`

Finally, we calculate the acceleration:

`\begin{gathered} a=(v)/(t) \\ \\ \text{ We replacing:} \\ \\ a=(10970)/(0.0401)=273566.08\text{ m/s}^2 \end{gathered}`

To get in terms of dividing the acceleration by g = 9.8 m/s², we get

`\begin{gathered} (a)/(g)=(273566.08)/(9.8) \\ \\ a=27914.9\text{ }g \end{gathered}`