Derive an expression for recoil velocity of gun.

1.	Derive an expression for recoil velocity of gun.
Answer» Let m_g be mass of gun, \(\vec v_g\) = recoil velocity of gun, m_bbe mass of Bullet \(\vec v_b\) Initial momentum = 0, Final momentum = m_g \(\vec v_g\) + m_b \(\vec v_b\) By law of conservation of momentum 0 = mg \(\vec v_g\) + m_b \(\vec v_b\) ⇒ \(\vec v_b\) = - \((\frac {m_b \vec v_b}{\vec m_g})\).

Answer»

Let m_g be mass of gun,

\(\vec v_g\) = recoil velocity of gun,

m_bbe mass of Bullet \(\vec v_b\)

Initial momentum = 0,

Final momentum = m_g \(\vec v_g\) + m_b \(\vec v_b\)

By law of conservation of momentum

0 = mg \(\vec v_g\) + m_b \(\vec v_b\)

⇒ \(\vec v_b\) = - \((\frac {m_b \vec v_b}{\vec m_g})\).

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