Question

The height, h in feet, of a rocket is given by h=-16t^2+64t+190, where t is time in seconds. Find the maximum height of the rocket and find the time the rocket was in the air.

Answer 1

Step-by-step explanation:

The height, h in feet, of a rocket is given by, where t is time in seconds.

$h=-16t^2+64t+190$ ...(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 $\dfrac{dh}{dt}=0$

$\dfrac{d(-16t^2+64t+190)}{dt}=0\\\\-32t+64=0\\\\t=\dfrac{64}{32}\\\\t=2\ s$

So, it will reach its maximum height in 2 seconds.

Now put t = 2 in equation (1) as follows :

$h(2)=-16(2)^2+64(2)+190\\\\=254\ \text{feet}$

So, the maximum height of the rocket and find the time the rocket was in the air is 254 feet and 2 seconds respectively.