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,

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

Explanation:

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

Differentiate the function with respect to x.

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

For maximum and minimum,

$\begin{gathered} -32t+144=0 \\ t=\frac{144}{32} \\ =4.5 \end{gathered}$

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.