A Nerf gun is shot straight up from the ground with an initial velocity of 14.0 m/s. What is the total time the projectile is in the air? PLEASE SHOW WORK WILL MARK BRAINLIEST

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

we need to know the time interval during which the force acts. impulse of force = momentum change