Time in the Air

Caught at the same height, the ball takes as long to come down as to go up:

$$t_{\text{air}} = \frac{2 v_0}{g}$$

Up and down take the same time: $2\ \mathrm{s}$ each, $4\ \mathrm{s}$ in the air.

At every height the speed is the same going up and coming down. The ball comes back with the launch speed pointing down: $\relax v = -v_0$.