Question

A gun of mass 15 kg fires a bullet shell
of mass 300 g with velocity of 100 m/s.
The recoil velocity of gun is​

Answer 1

$\huge\underline{ \red { \boxed{ \tt{to \: find}}}}$

$\tt{the \: recoil \: velocity \: of \: the \: gun}$

Given:

$\tt{ \bull \: mass \: of \: gun = 15 \: kg}$

$\tt{ \bull \: mass \: of \: bullet \: = 300 \: g}$

$\tt{ \bull \:initial \: velocity \: of \: bullet = 100 \frac{m}{s} }$

Formula To be used :

$\tt{ \bull{ \: momentum = mass \times velocity}}$

Solution :

$\tt{as \: we \: know \: : }$

$\tt{1 \: kg \: = 1000 \: g}$

$\tt{ \implies \: 300 \: g \: = \frac{300}{1000} kg}$

$\tt{ \implies \: 300g = 0.3 \: kg}$

$\tt{we \: know \: that \: : }$

$\tt{momentum \: = mass \times velocity}$

$\tt{momentum \: of \: bullet = 0.3 \times 100}$

$\implies \tt{momentum = 30}$

Recoil Velocity = Mass of gun/ momentum

$\tt { \implies \: recoil \: velocity \: = \frac{15}{30} }$

$\implies \tt{recoil \: velocity = 0.5 \: m \: per \: s}$

hence, The recoil Velocity of gun = 0.5 m/s

Answer 2

Given:

A gun of mass 15 kg fires a bullet shell of mass 300 g with velocity of 100 m/s.

To find:

Recoil velocity of gun ?

Calculation:

• Let final velocity of gun be v_(2).

• Initial momentum of both gun and bullet is zero.

Applying CONSERVATION OF LINEAR MOMENTUM principle:

$\sf m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}$

$\sf \implies 0 + 0 = ( \dfrac{300}{1000} \times 300) + 15v_{2}$

$\sf \implies 0 = 90 + 15v_{2}$

$\sf \implies 15v_{2} = - 90$

$\sf \implies v_{2} = - 6 \: m {s}^{ - 1}$

So, recoil velocity of gun is 6 m/s .