If you're shooting it from the ground, you can just find the total time in the air and divide by two.
We start with the equation yf = (-1/2)gt2 + v0t + y0.
Plugging in our values, we get 0 = (-1/2)(9.81)t2 + 23.4t.
This can then be factored, and we can solve for each factor: 0 = t [ (-1/2)(9.81)t + 23.4 ]
The 't' outside just gives us zero, which is the initial time (i.e. the beginning of the problem), so we can ignore it.
Solving for the other factor, we get:
(-1/2)(9.81)t + 23.4 = 0
==> -4.905t + 23.4 = 0
==> -4.905t = -23.4
==> t = 4.77 seconds.
Half of this is 2.39 seconds. Tada!