Question

At t seconds after launch is given by the function… how long will it take the rocket to reach its maximum height? What is the maximum height?

Answer 1

Given:

The height equation is,

`h(t)=-16t^2+144t+6`

Step-by-step explanation:

For maximum/minimum of a function, the first derivative of function is 0.

Differentiate the function with respect to x.

`\begin{gathered} (d)/(dt)h(t)=(d)/(dt)(-16t^2+144t+6) \\ =-32t+144 \end{gathered}`

For maximum and minimum,

`\begin{gathered} -32t+144=0 \\ t=(144)/(32) \\ =4.5 \end{gathered}`

So rocket reach it maximum height after 4.5 seconds of launch.

Substitute 4.5 for t in the equation to determine the maximum reached by rocket.

`\begin{gathered} h(4.5)=-16(4.5)^2+144\cdot4.5+6 \\ =-324+648+6 \\ =330 \end{gathered}`

So maximum height of rocket is 330 feet.