Answer
The recoil speed of the rifle is $1.82~m/s$
Work Step by Step
We can assume the initial momentum of the system is zero. By conservation of momentum, if the bullet gains a certain momentum $p_b$ in one direction, the rifle will gain the same magnitude of momentum $p_r$ in the opposite direction.
We can find the recoil speed $v_r$ of the rifle:
$p_r = p_b$
$m_r~v_r = m_b~v_b$
$v_r = \frac{m_b~v_b}{m_r}$
$v_r = \frac{(0.010~kg)(820~m/s)}{4.5~kg}$
$v_r = 1.82~m/s$
The recoil speed of the rifle is $1.82~m/s$.
