Novelist JV

The French novelist Jules Verne wrote a novel in which the idea was expressed of sending to the moon a large cannon shell with a human crew inside. The cannon barrel, from which the shell was fired, had a length of 220 m.

a) How long would the shell move inside the barrel, if it were to fly out of it at the second cosmic velocity of 11.2 km/s?
b) What would their acceleration be when moving inside the barrel?
c) How long a cannon barrel would have to be, if the shell were to fly out of it at a speed of 11.2 km/s and move inside the barrel with an acceleration of 100 m/s²? This acceleration is still acceptable for cosmonauts.

Final Answer:

t₁ =  0.0393 s
a₁ =  285090.9091 m/s²
s₂ =  627200 m

Step-by-step explanation:

$$\begin{gathered} v=11.2\cdot 1000=11200\text{m/s} \\ s=220\text{m} \\ s=\frac{1}{2}\cdot a\cdot t_1^2 \\ s=\frac{1}{2}\cdot (v/t_1)\cdot t_1^2 \\ 2\cdot s=v\cdot t_1 \\ {t}_1=\frac{2\cdot s}{v}=\frac{2\cdot 220}{11200}=0.0393\text{s} \end{gathered}$$

$a_1=\frac{v}{t_1}=\frac{11200}{0.0393}=285090.9091{\text{m/s}}^2\doteq 2.851\cdot 10^5{\text{m/s}}^2$

$$\begin{gathered} a_2=100{\text{m/s}}^2 \\ v=a_2\cdot t_2 \\ {t}_2=v/a_2=11200/100=112\text{s} \\ {s}_2=\frac{1}{2}\cdot a_2\cdot t_2^2=\frac{1}{2}\cdot 100\cdot 112^2=627200\text{m} \end{gathered}$$

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