Question

A bullet when first into a target loses half of its velocity after penetrating $20cm$. Further distance of penetration before it comes to rest is

• A. $6.66cm$
• B. $3.33cm$
• C. $12.5cm$
• D. $10cm$
• E. $5cm$

Answer 1

The correct option is A

$6.66cm$

Step 1: Given data

Distance, $s=20cm$

Initial velocity after penetrating distance $20cm$ $=u$

Final velocity after penetrating distance $20cm$$=\frac{u}{2}$

Distance of penetration before it comes to rest $=xcm$

Initial velocity before it comes to rest $=\frac{u}{2}$

Final velocity before it comes to rest $=0$

Acceleration $=a$

Step 2: Find the distance covered before rest

From the equation of motion

$v^2=u^2+2as$

Case 1: Velocity becomes half

$$\begin{gathered} \frac{u^2}{4}=u^2-2ax20 \\ \frac{3}{4}{u}^2=40a \\ \Rightarrow a=\frac{3}{160}{u}^2 \end{gathered}$$

Case 2: Final velocity became zero

$v^2=u^2+2as$

$0=(u^2/4)-2a\left(20+x\right)$

Solving for $x$, we get

$x=6.66cm$

Hence, option A is correct.