To find the time of flight, determine the time the projectile takes to reach maximum height. The time of flight is just double the maximum-height time.

Start with the equation:

v_y = v_oy + a_y t

At maximum height, v_y = 0.

The time to reach maximum height is t_1/2 = - v_oy / a_y

Time of flight is t = 2t_1/2 = - 2v_oy / a_y

Plugging in v_oy = v_o sin(q) and a_y = -g, gives:

Time of flight is t = 2 v_o sin(q) / g

where g = 9.8 m/s²

The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.