Answer
$v_{com} = (10.0~m/s)~\hat{i}$
Work Step by Step
Since Particle 2 always stays directly above Particle 1, they must have the same horizontal velocity of $10.0~m/s$.
When the center of mass reaches maximum height, the horizontal velocity of both particles is $10.0~m/s$ while the vertical velocity of both particles is $0$.
We can write the velocity of the center of mass in unit-vector notation:
$v_{com} = (10.0~m/s)~\hat{i}$
