Answer:
The height of the rocket after 3 seconds = 183 feet
Step-by-step explanation:
Given:
Rocket is initially launched from a height of 36 feet.
Initial speed of the rocket = 97 ft/s
The height of the rocket at any time
in seconds is given as:
![-16t^2+97t+36](https://tex.z-dn.net/?f=-16t%5E2%2B97t%2B36)
To find the height of the rocket after 3 seconds.
Solution:
The height function of the rocket is:
![h(t)=-16t^2+97t+36](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%2B97t%2B36)
In order to find the height of the rocket after
seconds we plugin
in the function.
![h(3)=-16(3)^2+97(3)+36](https://tex.z-dn.net/?f=h%283%29%3D-16%283%29%5E2%2B97%283%29%2B36)
![h(3)=-16(9)+291+36](https://tex.z-dn.net/?f=h%283%29%3D-16%289%29%2B291%2B36)
![h(3)=-144+291+36](https://tex.z-dn.net/?f=h%283%29%3D-144%2B291%2B36)
![h(3)=183\ ft](https://tex.z-dn.net/?f=h%283%29%3D183%5C%20ft)
Thus, height of the rocket after 3 seconds = 183 feet.