Question

A bullet of mass 50 g is fired from a rifle of mass 4 kg.38 M/S is released with initial velocity Calculate the recoil velocity of the rifle.​

Answer 1

$\large{\underline{\underline{ \bf{⎆Question:-}}}}$

• A bullet of mass 50 g is fired from a rifle of mass 4 kg . 38 M/S is released with initial velocity Calculate the recoil velocity of the rifle.

$\large{\underline{\underline{ \bf{☂ Solution:-}}}}$

$\bold{ \small \underline{ \mathbb{\underline{GIVEN : }}}}$

• Mass of bullet ( m ) = 50 grams = 0.05 kg
• Mass of rifle ( m' ) = 4 kilograms
• Initial velocity ( u ) = 38m/s

$\bold{ \small \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• The recoil velocity of the rifle (v)

$\bold{ \small \underline{ \mathbb{\underline{HERE : }}}}$

$\tt{ Since \: the \: rifle \: was \: at \: rest \: , \: initially }$

$\tt{ Therefore \: , \: initial \: velocity \: (u) \: = \: 0 \: m/s }$

$\tt{ ➥ Total\:initial\:momentum\:of\:the\:rifle\:with\:bullet\:after\:firing\::}$

$\longmapsto (m × u) + (m' × v)$

$\longmapsto( 0.05 )× 38 +( 4 × v)$

$\longmapsto1.9 +( 4 v)$

• According to the law of conservation of momentum :

$\tt{ ➫ Total \: momentum \: after \: the \: firing \: = \: Total \: momentum \: before \: the \: firing \: }$

$∴ \: 4v \: + \: 1.9 \: = \: 0$

$\longmapsto \: 4v \: = \: - 1.9$

$\longmapsto \:v = \: - 0.475$

• So , the recoil velocity of rifle is -0.475 m/s