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 [tex]t[/tex] in seconds is given as:
[tex]-16t^2+97t+36[/tex]
To find the height of the rocket after 3 seconds.
Solution:
The height function of the rocket is:
[tex]h(t)=-16t^2+97t+36[/tex]
In order to find the height of the rocket after [tex]t[/tex] seconds we plugin [tex]t=3[/tex] in the function.
[tex]h(3)=-16(3)^2+97(3)+36[/tex]
[tex]h(3)=-16(9)+291+36[/tex]
[tex]h(3)=-144+291+36[/tex]
[tex]h(3)=183\ ft[/tex]
Thus, height of the rocket after 3 seconds = 183 feet.
