Question

A bullet of mass $20g$ has an initial speed of $1m/s$, just before it starts penetrating a mud wall of thickness $20cm$. if the wall offers a mean resistance of $2.5\times {10}^{-2}N$, the speed of the bullet after emerging from the other side of the wall is close to:

• A. $0.4m/s$
• B. $0.1m/s$
• C. $0.3m/s$
• D. $0.7m/s$

Answer 1

The correct option is D

$0.7m/s$

Step 1: Given

Mass, $m=20g=20\times {10}^{-3}Kg$

Initial speed, $u=1m/s$

Thickness of the wall, $s=20cm=20\times {10}^{-2}m$

Force, $F=-2.5\times {10}^{-2}N$(-ve sign as the force is resistive)

Step 2: Determine the acceleration

Force is given by, $F=ma$

Hence, the acceleration a is given by

$\Rightarrow a=\frac{F}{m}$

$$\begin{gathered} a=\frac{-2.5\times {10}^{-2}}{20\times {10}^{-3}} \\ =-1.25m/s^2 \end{gathered}$$

The value is negative as the body is decelerating.

Step 3: Determine the final velocity

Using the third equation of motion to determine the final velocity, $v$

$$\begin{gathered} v^2=u^2+2as \\ ={\left(1\right)}^2+2(-1.25)(20\times {10}^{-2}) \\ {v}^2=0.5 \\ v=0.7 \end{gathered}$$

Hence, option D is the correct option.