Decelerated 80572

A projectile was weighing 20 g shoots at a speed of 800 m. with -1 being dug 100 mm deep into the masonry. How long does it brake in masonry assuming uniformly decelerated motion?

Correct answer:

t =  0.0003 s

Step-by-step explanation:

$$\begin{gathered} m=20\text{g} \\ v=800\text{m/s} \\ s=100\text{mm}\to \text{m}=100:1000\text{m}=0.1\text{m} \\ E=\frac{1}{2}\cdot m\cdot v^2=\frac{1}{2}\cdot 20\cdot 800^2=6400000\text{J} \\ s=\frac{1}{2}\cdot a\cdot t^2 \\ v=a\cdot t \\ s=\frac{1}{2}\cdot v\cdot t \\ t=2\cdot s/v=2\cdot \frac{1}{10}/800=\frac{1}{4000}\doteq 0.0003\text{s} \\ \text{ Verifying Solution: } \\ a=v/t=800/0.0003=3200000{\text{m/s}}^2 \\ {s}_2=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot 3200000\cdot 0.0003^2=\frac{1}{10}=0.1\text{m} \end{gathered}$$

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