Question

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?

Answer 1

Answer:

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