Question

Bullets of mass $10g$ each are fired from a machine gun at a rate of $6$ bullets/minute. The muzzle velocity of bullets is $100m/s$. The thrust force (in $N$) due to firing bullets experienced by the person holding the gun stationary is ${10}^{-x}$. Find $x$.

Answer 1

Given,

Mass of each bullet, $m=10g$

$m=\frac{10}{1000}=0.01kg$

Time taken by the gun to fire 6 bullets, $T=1min=60s$

Time taken by the gun to fire 1 bullet, $t=\frac{T}{6}$

$t=\frac{60}{6}$

$t=10s$

Initial velocity, $u=0$

Final velocity, $v=100m/s$

Acceleration, $a=\frac{v-u}{t}$

$a=\frac{100-0}{10}$

$a=10m/s^2$

Force, $F=m\times a$

$F=0.001\times 10$

$F=0.1N={10}^{-1}N$

According to Newton's third law, to every action, there is an opposite and equal reaction.

The thrust force due to firing bullets experienced by the person holding the gun stationery is ${10}^{-1}N$

$x=1$