Arocket is launched upward so that its distance, in feet, above the ground after t seconds is represented by the function below. what is its maximum height? h(t)=−16t2+320t

1600 feet.

Step-by-step explanation:

Given : A rocket is launched upward so that its distance, in feet, above the ground after t seconds is represented by the function

To find : its maximum height.

First we differentiate the given function , we get

Put  , we get

Hence, at t=10 , rocket achieves its maximum height.

Hence, its maximum height = 1600 feet.

1600 ft

Step-by-step explanation:

We are given that a rocket is a launched upward so that its distance(feet) above the ground after t seconds is represented by the function

We have to find the maximum height.

Substitute h(t)=0

When t=0 it means the rocket is at ground launch.

When t= 20 s.

Total time taken by rocket=20 s.

Half of the time taken to reach maximum height and half of the time taken to reach ground  back.

Therefore, time taken by rocket to reach maximum height=

Substitute t=10 in given function

Then we get

h(10)=-16(10)^2+320(10)=-1600+3200=1600 ft[/tex]

Hence, the maximum height=1600 ft

i think the correct option is the second option.