Question

A gun of mass 3 kg fires a bullet of mass 30 g. The bullet takes 0.003 s to move through the barrel of the gun
and acquires a velocity of 100 m/s. Calculate :
(1) the velocity with which the gun recoils.
(ii) the force exerted on gunman due to recoil of the gun​

Answer 1

$\Huge{\fbox{\underline{\mathfrak{Answer :-}}}}}$

The velocity of the gun is 1 m/s.

The Force exerted on the gunman while the recoiling of gun is 1000N.

$\huge\underline\mathtt {Given :-}$

Mass of gun =3 kg = ${m_{1}$

Mass of bullet=30 g=0.03 kg = $m_{2}$

Velocity of bullet=100 m/s = $v_{2}$

Time taken by the bullet = 0.003 s

$\large \fbox{ \: \sf {Solution :-} \: \sf \underline}$

According to the law of conservation of momentum we have

$m_{1} v_{1}=m_{2} v_{2}$

Substitute the values of $m_{1}, m_{2}, v_{2}$ in the above expression

$3 \times v_{1}=0.03 \times 100\\\\3 v_{1}=3\\\\v_{1}=\frac{3}{3}=1$

Hence, $v_{1} =1m/s$

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

$=100-\frac{0}{0.003}$

=33333.33m/s

The velocity of the given gun is 33333.33 m/s.

To find the force we have  

F = m x a

Where, m = 0.03

a = 33333.33

By substituting the values

= (0.03) x (33333.33)  

= 1000N

Answer 2

• The velocity with which the gun recoil is$\sf - 1 \: m/s^{2}$

• The force exerted on gun man due to recoil of the gun is 1000 N.

GIVEN :

• Mass of gun = 3 kg.
• Mass of bullet = 30 g.
• Time, t = 0.003 sec.
• Velocity, v = 100 m/s.

TO CALCULATE :

• The velocity with which the gun recoils.
• The force exerted by the gun man due to recoil of the gun.

FORMULA :

$\sf Force \: = \: \dfrac {\Delta p}{\Delta t}$

SOLUTION :

Net force on gun and bullet, system is zero.

$\hookrightarrow \sf 3 \: \times \: v \: (30 \times 10^{-3}) \: \times 100 \: = \: 0$

$\hookrightarrow \sf 3v \: = \: - (30 \: \times \: 10^{-1}$

$\therefore \boxed{\sf V \: = \: - 1 \: m/s^{2}}$

$\bold{Force \: = \: \dfrac {\Delta p}{\Delta t}}$

$\hookrightarrow↪ \sf \dfrac {m(v \: - \: 0)}{0.003}$

$\hookrightarrow↪ \sf \dfrac {3 \: \times \: 1}{0.003}$

$\therefore \boxed{\sf F \: = \: 1000 \: N}$

hope help u mate ✌