We can determine the time in the air by the initial vertical velocity component Vyo.To get the Vyo this is the formula;
Vyo = 15.9 sin(30)
Vyo = 7.95 m/s
So, the initial vertical velocity component vyo is 7.95 m/s
Vy becomes zero at
t = Voy/g
t = 7.95 m/s / 9.8 m/s^2
t = 0.81 s
It is 0.81 s long that the catapult is in the air.