The projectile has a height h at time t given by
h = (14.0 m/s) t - 1/2 g t ²
where g = 9.80 m/s² is the magnitude of the acceleration due to gravity. Solve for t when h = 0 :
0 = (14.0 m/s) t - 1/2 g t ²
0 = 1/2 t (28.0 m/s - g t )
1/2 t = 0 or 28.0 m/s - g t = 0
The first equation says t = 0, which refers to the moment the gun is first fired, so we ignore that solution. We're left with
28.0 m/s - g t = 0
t = (28.0 m/s) / g
t = (28.0 m/s) / (9.80 m/s²)
t ≈ 2.86 s
