Answer:
This is an example of completely inelastic collision, since they grab each other and move as a single object after the collision.
The conservation of momentum requires
[tex]\vec{P_1} + \vec{P_2} = \vec{P}_{final}[/tex]
where
[tex]\vec{P_1} = m_1v_1 \^x\\\vec{P_2} = m_2v_2 \^y[/tex]
Their final momentum is
[tex]\vec{P}_{final} = m_1v_1 \^x + m_2 v_2 \^y[/tex]
Their final velocity and direction is
[tex]\vec{v}_{final} = \frac{m_1v_1}{m_1 + m_2}\^x + \frac{m_2v_2}{m_1 + m_2}\^y[/tex]
Although not states in the question, let's consider the case that the masses and speeds of the eagles are the same:
[tex]\vec{v}_{final} = \frac{v}{2}\^x + \frac{v}{2}\^y[/tex]
