Question

bullet of mass 10 g is fired from a gun of mass 6 kg with a velocity of 300 m/s. calculate the recoil velocity of the gun. ​

Answer 1

Given:-

• Mass of bullet is 10g .
• Mass of gun is 6kg.
• Velocity of bullet is 300m/s.

To Find:-

• The recoil velocity of gun .

Formula Used:-

We will make use of concept of law of conservation of momentum.

$\large{\underline{\boxed{\red{\tt{\dag m_1v_1+m_2v_2=m_1u_1+m_2u_2.}}}}}$

Calculation:-

Here as per given data ,

• $\tt{ m_1=10g \:and\: m_2=6kg}$
• $\tt{v_1=300m/s \:and\:v_2=?}$
• $\tt{u_1=u_2=0m/s.}$

On putting the values in power formula stated,

$\tt{\implies m_1u_1+m_2u_2=m_1v_1+m_2v_2 }$

$\tt{\implies 10g\times0+6\times 0=10g\times 300+6kg\times v_2}$

$\tt{\implies 0 = 0.01\times300+6v_2 }$

$\tt{\implies 6v_2=(-3)}$

$\tt{\implies v_2=\dfrac{\cancel{-3}}{\cancel{6}}}$

$\underline{\boxed{\red{\tt{\longmapsto v_2=-0.5m/s}}}}$

Hence the recoil velocity of gun is 0.5 m/s.

Answer 2

Given:

A bullet of mass 10 g is fired from a gun of mass 6 kg with a velocity of 300 m/s.

To find:

Recoil velocity ?

Calculation:

• Let final velocity of gun be v_(g):

• Also, initial velocity of both bullet and gun is zero.

$\rm m_{b}u_{b} + m_{g}u_{g} = m_{b}v_{b} + m_{g}v_{g}$

$\rm \implies 0 + 0 = ( \frac{10}{1000} \times 300)+ 6v_{g}$

$\rm \implies 6v_{g} = - 3$

$\rm \implies v_{g} = - 0.5 \: m {s}^{ - 1}$

So, recoil velocity of gun is 0.5 m/s

• Negative sign indicates that recoil velocity is in opposite direction to the velocity of bullet.