The height h in feet of the ball t seconds after it is kicked can be modeled by the function h = - 4t (4t - 11). How long is the football in the air?

t₁ = 2,75 sec

Step-by-step explanation:

The ball will get h maximum when dh/dt (its vertical component of the speed is equal to 0. At this moment the ball has flown half of the total flight time

Then

h (t) = - 4t * (4*t - 11)

h (t) = - 16*t² + 44*t

Taking derivatives on both sides of the equation we get:

dh/dt = - 32*t + 44

dh/dt = 0 ⇒ - 32*t + 44 = 0

t = 44/32 ⇒ t = 1,375 s

So twice this time

2*t = 2 * 1.375

Total time t₁ = 2,75 sec