Question

A bullet fired into a wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of

• A. $\frac{22}{3}$ cm
• B. $\frac{40}{3}$ cm
• C. $\frac{20}{3}$ cm
• D. $\frac{22}{5}$ cm

Answer 1

Answer: (B)

$\frac{40}{3}$ cm

Let initial velocity $=V$

When bullet pennetrates $0.4m=\frac{V}{2}$

& let dist $=x$ (when $V_{final}=0$)

Applying, eq. of kinematic motion

$\frac{V^2}{4}=V^2-2a\left(0.4\right)$ {$a$ is de-acc $a\to (-)ve$)

$a=\frac{{3V}^2}{4\times 0.8}⟶\left(i\right)$

Now, $0=\frac{V^2}{4}-2a\left(x\right)$

$2ax=\frac{V^2}{4}⟶\left(ii\right)$

Putting $\left(i\right)$ in $\left(ii\right)$

$\frac{{3V}^{2}a}{4\times 0.8}=\frac{V^2}{8x}$

$\Rightarrow x=\frac{0.4m}{3}$

$x=\frac{40}{3}cm$