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Sagot :
Initially, the system is at rest therefore, the initial momentum of the system is zero.
The final momentum of the system can be expressed as,
[tex]p_f=m_1v_1+m_2v_2[/tex]According to conservation of momentum,
[tex]p_i=p_f[/tex]Plug in the known expressions,
[tex]\begin{gathered} 0=m_1v_1+m_2v_2 \\ m_1v_1=-m_2v_2 \\ v_1=-\frac{m_2}{m_1}v_2 \end{gathered}[/tex]Substitute the known values,
[tex]\begin{gathered} v_1=-\frac{(69.4\text{ g)(}\frac{1\text{ kg}}{1000\text{ g}})}{(2.6\text{9 kg)}}(650\text{ m/s)} \\ =-16.8\text{ m/s} \end{gathered}[/tex]Thus, the recoil velocity of gun is -16.8 m/s where negative sign indicates that the motion of rifle is in the opposite direction of the bullet.
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