Aknight of the round table fires off a vat of burning pitch from his catapult at 15.9 m/s, at 30 ◦ above the horizontal. the acceleration of gravity is 9.8 m/s2 . how long is it in the air?

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.

Ithink it is letter b, i may be wrong but i think that is the answer