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

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:

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

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

$\begin{gathered} V=\frac{d}{t} \\ \\ t=\frac{d}{V} \\ \\ \text{ we replacing:} \\ \\ t=\frac{220}{5485}=0.0401\text{ s} \end{gathered}$

Finally, we calculate the acceleration:

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

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

$\begin{gathered} \frac{a}{g}=\frac{273566.08}{9.8} \\ \\ a=27914.9\text{ }g \end{gathered}$