Shot

Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm.

What is the average force of resistance of wood?

Correct result:

F =  5636.1 N

Solution:

$$\begin{gathered} s=25cm=0.25m \\ m=43g=0.043kg \\ v=256m\mathrm{/}s \\ F=ma \\ a=v\mathrm{/}t \\ s={\displaystyle \frac{1}{2}}a{t}^2={\displaystyle \frac{1}{2}}vt \\ t={\displaystyle \frac{2h}{v}}={\displaystyle \frac{2\cdot 25\mathrm{/}100}{256}}=0.001953s \\ a={\displaystyle \frac{v^2}{2h}}={\displaystyle \frac{256^2}{2\cdot 25\mathrm{/}100}}=131072m\mathrm{/}{s}^2 \\ F=ma=43\mathrm{/}1000\cdot 131072=5636.1\text{ N} \end{gathered}$$

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