From a rifle of mass $4\ kg$, a bullet of mass $50\ g$ is fired with an initial velocity of $35\ m/s$. Calculate the initial recoil velocity of the rifle.

Mass of the bullet $m_1=50\ g=\frac{50}{1000}\ kg.=0.05\ kg.$

Mass of the rifle $m_2=4\ kg.$

Initial velocity of the bullet $u_1=35\ m/s$

Final velocity of the bullet $v_1=0$

Final velocity of the rifle $v_2=0$

Let the recoil initial velocity of the rifle $u_2=0$

According to the law of the conservation of momentum,

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

Or $0.05\times 35+4\times u_2=0.05\times0+4\times0$

Or $1.75+4u_2=0+0$

Or $4u_2=-1.75$

Or $u=-\frac{1.75}{4}$

Or $u=-0.4375\ m/s$

Therefore, the initial recoil velocity of the rifle $0.4375\ m/s$ in the opposite direction.

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Updated on: 10-Oct-2022

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