#### Answer

The bird's speed just after swallowing the insect is 4.8 m/s

#### Work Step by Step

We can use conservation of momentum to find the final speed $v_f$ of the bird. Let $m_b$ be the mass of the bird. Let $m_i$ be the mass of the insect. Let's consider the system of the bird and the insect.
$p_f = p_0$
$(m_b+m_i)~v_f = m_b~(6.0~m/s)+m_i~(-30~m/s)$
$v_f = \frac{m_b~(6.0~m/s)+m_i~(-30~m/s)}{m_b+m_i}$
$v_f = \frac{(0.30~kg)(6.0~m/s)+(0.010~kg)(-30~m/s)}{0.30~kg+0.010~kg}$
$v_f = 4.8~m/s$
The bird's speed just after swallowing the insect is 4.8 m/s.