Answer :
We have
mr=mass rifle
mb=mass bullet
vb0=initial velocity of the bullet
vr0=initial velocity of the rifle
vbf=final velocity of the bullet
vrf=final velocity of the rifle
mr=2.68 kg
mb=69.5 g =0.0695 kg
vb0=0 m/s
vr0=0m/s
vbf=612 m/s
vrf=?
[tex]m_bv_{bo}+m_rv_{ro}=m_bv_{bf}+m_rv_{rf}[/tex][tex]0=m_bv_{bf}+m_rv_{rf}[/tex]we isolate the vr
[tex]v_{rf}=\frac{-m_bv_{bf}}{m_r}[/tex]Then we substitute
[tex]v_{rf}=\frac{-(0.0695\operatorname{kg})(612)}{2.68}=-15.871\text{ m/s}[/tex]The recoil velocity is -15.871 m/s