If two balls are tossed simultaneously into the air, the...

Let the masses of the two balls be $m_1$ and $m_2$.

While in flight, the only force acting on each ball is gravity (ignoring air resistance).

The acceleration of the first ball is $\vec{a}_1 = \vec{g}$ and the acceleration of the second ball is $\vec{a}_2 = \vec{g}$.

The acceleration of the centre of mass of the two balls is given by:

$\vec{a}_{cm} = \dfrac{m_1 \vec{a}_1 + m_2 \vec{a}_2}{m_1 + m_2}$

Substituting $\vec{a}_1 = \vec{g}$ and $\vec{a}_2 = \vec{g}$:

$\vec{a}_{cm} = \dfrac{m_1 \vec{g} + m_2 \vec{g}}{m_1 + m_2} = \dfrac{(m_1 + m_2)\vec{g}}{m_1 + m_2} = \vec{g}$

Thus, the acceleration of their centre of mass is equal to $g$ downwards, independent of their masses, speeds, or directions of motion.