# 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:

$s = 25 \ cm = 0.25 \ m \ \\ m = 43 \ g = 0.043 \ kg \ \\ v = 256 \ m/s \ \\ \ \\ F = ma \ \\ a = v/t \ \\ s = \dfrac12at^2 = \dfrac12vt \ \\ t = \dfrac{ 2 h }{ v} = \dfrac{ 2 \cdot 25/100 }{ 256} = 0.001953 \ s \ \\ a = \dfrac{ v^2}{ 2h } = \dfrac{ 256^2}{ 2 \cdot 25/100 } = 131072 \ m/s^2 \ \\ F = ma = 43/1000 \cdot 131072 = 5636.1 \ \text{N}$

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