Question

A soldier fires a bullet from his rifle towards the target wall. If the mass of the bullet is $30g$ and its velocity on leaving the gun is $1080km{h}^{-1}$. Find the magnitude of the average resistance force applied by the target wall to stop the bullet in $0.2$ seconds.

• A. $50N$
• B. $45N$
• C. $40N$
• D. $55N$

Answer 1

The correct option is B $45N$

Given:
Mass of bullet $\left(m\right)$ = $30g$ = $0.03kg$
Initial velocity of the bullet $\left(v_i\right)$
= $1080km{h}^{-1}$ = $\frac{1080\times 5}{18}$ = $300m{s}^{-1}$
Final velocity of the bullet $\left(v_f\right)$ = 0
Time taken by the bullet $\left(t\right)$ = $0.2$ sec

According to the second law of motion,
$\Rightarrow$$Force=\frac{\Delta p}{\Delta t}$
Change in momentum of the bullet:
$\Rightarrow$ $m(v_f-v_i)$ = $-m{v}_i$
$\Rightarrow$ $Force=\frac{\Delta p}{\Delta t}$ $=\frac{-m{v}_i}{\Delta t}$
$\Rightarrow$ $\frac{-0.03kg\times 300m{s}^{-1}}{0.2sec}$ = $45N$