Question 70: Work, Energy and Power & Circular Motion

Question

A bullet is fired into a fixed target looses one third of its velocity after travelling $$4 \mathrm{~cm}$$. It penetrates further $$\mathrm{D} 	imes 10^{-3} \mathrm{~m}$$ before coming to rest. The value of $$\mathrm{D}$$ is :

Accepted Answer

$$\begin{aligned}
& v^2-u^2=2 a S \
& \left(\frac{2 u}{3}ight)^2=u^2+2(-a)\left(4 	imes 10^{-2}ight) \
& \frac{4 u^2}{9}=u^2-2 a\left(4 	imes 10^{-2}ight) \
& -\frac{5 u^2}{9}=-2 a\left(4 	imes 10^{-2}ight) \ldots(1) \
& 0=\left(\frac{2 u}{3}ight)^2+2(-a)(x) \
& -\frac{4 u^2}{9}=-2 a x \ldots(2)
\end{aligned}$$
$$(1)/(2)$$
$$\begin{aligned}
& \frac{5}{4}=\frac{4 	imes 10^{-2}}{\mathrm{x}} \
& \mathrm{x}=\frac{16}{5} 	imes 10^{-2} \
& \mathrm{x}=3 \cdot 2 	imes 10^{-2} \mathrm{~m} \
& \mathrm{x}=32 	imes 10^{-3} \mathrm{~m}
\end{aligned}$$

Answer

23

Answer

32

Answer

42

Answer

52

Work, Energy and Power & Circular Motion

A bullet is fired into a fixed target looses one third of its velocity after travelling $4 \mathrm{~cm}. It penetrates further \mathrm{D} \times 10^{-3} \mathrm{~m} before coming to rest. The value of \mathrm{D}$ is :

Choose the correct answer: