Answer:
Maximum height of the rocket = 1194.39 feet.
Step-by-step explanation:
The equation that shows the height of the rocket, y in feet, is related to the time after launch, x in seconds is as follows :
[tex]y=-16x^2+261x+130[/tex] ...(1)
We need to find the maximum height reached by rocket. For maximum height,
[tex]\dfrac{dy}{dx}=0\\\\\dfrac{d(-16x^2+261x+130)}{dx}=0\\\\-32x+261=0\\\\x=\dfrac{261}{32}\\\\x=8.15\ s[/tex]
Put x = 8.15 s in equation (1).
[tex]y=-16(8.15)^2+261(8.15)+130\\\\y=1194.39\ \text{feet}[/tex]
So, the maximum height of the rocket is 1194.39 feet.
