Step-by-step explanation:
The height, h in feet, of a rocket is given by, where t is time in seconds.
[tex]h=-16t^2+64t+190[/tex] ...(1)
We need to find the maximum height of the rocket and find the time the rocket was in the air. For maximum height, put [tex]\dfrac{dh}{dt}=0[/tex]
[tex]\dfrac{d(-16t^2+64t+190)}{dt}=0\\\\-32t+64=0\\\\t=\dfrac{64}{32}\\\\t=2\ s[/tex]
So, it will reach its maximum height in 2 seconds.
Now put t = 2 in equation (1) as follows :
[tex]h(2)=-16(2)^2+64(2)+190\\\\=254\ \text{feet}[/tex]
So, the maximum height of the rocket and find the time the rocket was in the air is 254 feet and 2 seconds respectively.
