Question

A bullet of mass 5 g is fired from a gun weighing 5.0 kg. If the initial velocity of the bullet is 250 m s–1, calculate the velocity with which the gun recoils.

Answer 1

Answer:

Given:

Mass of gun = 5 kg

Mass of bullet = 5 g

Velocity of bullet = 250 m/s

To find:

Recoil Velocity of gun

Calculation:

Whenever the trigger of gun is pressed , the bullet leaves the muzzel of the gun with high velocity. Since the momentum pf the system is conserved , the gun experiences equal momentum change in the opposite direction.

Hence the gun recoils backwards. The velocity is called Recoil Velocity

Calculation:

As per Conservation of Momentum :

Initial Momentum = Final momentum

$= > 0 + 0 = \{( \frac{5}{1000} ) \times 250 \} + (5 \times v)$

$= > 5v = - \dfrac{5 \times 250}{1000}$

$= > v = - 0.25 \: m {s}^{ - 1}$

So final answer :

$\boxed{ \red{ \large{ \bold{Recoil \: Velocity = - 0.25 \: m {s}^{ - 1} }}}}$

Negative sign indicates opposite direction or recoil as compared to velocity of bullet.

Answer 2

Question :

A bullet of mass 5 g is fired from a gun weighing 5.0 kg. If the initial velocity of the bullet is 250 m s–1, calculate the velocity with which the gun recoils.

Theory :

Conservation of linear momentum :

If no external force acts on the system of constant mass the total momentum of the system remains constant .

Solution :

Let recoil velocity = v

Given :

bullet mass,m =5g = 0.005 kg

intital velocity,u = 250 m/s

Mass of Gun ,M = 5kg

Intital both bullet and gun are at rest

⇒Intial momentum before firing = 0

______________________________

As no external force acts on the system

So According to the law of conservation of Momentum .

Total momentum before firing = Total momentum after the firing

⇒0 = mu+ Mv

⇒Mv = -mu

⇒5× v = -0.005×250

$\implies \: v = \dfrac{ - 0.005 \times 250}{5}$

$\implies \: v = \dfrac{-5 \times 250}{5 \times 1000}$

$\implies \: v = - 0.25 \: ms {}^{ - 1}$

Therefore;

${\purple{\boxed{\large{\bold{Recoil\:Velocity =-0.25ms{}^{-1}}}}}}$

⇒The negative sign shows that v and u are in opposite directions i.e ,the gun gives a kick in the backward direction or gun recoils with velocity v.