Question

a bullet is fixed with a velocity 40 m/s from a gun of mass 4 kgwhat will be the recoil velocity of the gun if the mass of the bullet is 0.2 kg?​

Answer 1

Answer

• Mass of the gun = 4 kg
• Mass of the Bullet = 0.2 kg
• Velocity at which the bullet is being fixed = 40 m/s
• Initial Velocities =
• Recoil Velocity = ?

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$\quad$ ● Here we use the concept, "Conservation Of Momentum". Which tells us that Initial Momentum will be equal to the Final momentum.

$\quad$ ● Momentum is equal to the product of the Mass & Velocity (Momentum = Mass × Velocity)

$\sf :\implies Initial \ Momentum = Final \ Momentum$

$\sf :\implies m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

$\sf :\implies v_2 = \dfrac{(-m_1)v_1}{m_2}$

$\sf :\implies v_2 = \dfrac{(-0.2)\times 40}{4}$

$\sf :\implies v_2 = \dfrac{-8}{4}$

$\sf :\implies\underline{\boxed{\pink{\mathfrak{v_2 = -2 m/s}}}}$

$\displaystyle\therefore\: \underline{\textsf{Recoil Velocity is \textbf{ -2 m/s}}}$

Answer 2

Answer:

$\huge{ \underline{ \rm{ \large{ \pink{Given:}}}}}$

• Velocity which bullet being fixed = 40 m/s
• Mass of gun = 4 kg
• Mass of bullet = 0.2 kg

$\huge{ \underline{ \large{ \rm{ \red{Find:}}}}}$

• Recoil velocity???

$\huge{ \underline{ \large{ \rm{ \green{Solution:}}}}}$

• Here we are using the concept of conservation of momentum.

• The total momentum of the system is the same after the collision as before it as shown by the equation initial momentum = final momentum

• Intial momentum = Final momentum

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

${ \large{ { \to{ \sf{ v_{2} = \frac{( - m_{1}) v_{1} }{ m_{2} } }}}}}$

$\: \: \: \:$

${ \to { \large{ \sf{ v_{2} = \frac{( - 0.2) \times 40}{4} }}}}$

$\: \: \:$

${ \to{ \large{ \sf{ v_{2} = \frac{ - 8}{4} }}}}$

$\: \: \: \:$

${ \to{ \sf{ \large{ \blue{ v_{2} = - 2m/s}}}}}$

Therefore,

• Velocity of Recoil = -2m/s