What is recoil velocity?

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Solution

When you fire a bullet from the gun, the gun experience a force in the backward direction. Because of this force, the gun attains a velocity in the backward direction. This velocity is known as recoil velocity.

$P_{b e f o r e f i r e} = P_{a f t e r f i r e}$
${(M_{g} V_{g} + m_{b} v_{b})}_{b e f o r e f i r e} = {(M_{g} V_{g} + m_{b} v_{b})}_{a f t e r f i r e}$
${(M_{g} 0_{g} + m_{b} 0_{b})}_{b e f o r e f i r e} = {(M_{g} V_{g} + m_{b} (- v_{b}))}_{a f t e r f i r e}$
$0 = M_{g} V_{g} - m_{b} v_{b}$
$V_{g} = \frac{m_{b} v_{b}}{M_{g}}$

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