Question

Question 5Points 3A model rocket is projected straight upward from the ground level according to theheight equation h =-16f2 + 144t, t> 0, where h is the height in feet and t is the time inseconds. At what time is the height of the rocket maximum and what is that height?

Answer 1

Step 1:

Write the equation:

`h\text{ = -16t}^2\text{ + 144t}`

Step 2

`At\text{ maximum height, }(dh)/(dt)\text{ = 0}`

Step 3:

`\begin{gathered} h\text{ = -16t}^2\text{ + 144t} \\ \\ (dh)/(dt)\text{ = -32t + 144} \\ \\ 32t\text{ = 144} \\ t\text{ = }(144)/(32) \\ t\text{ = 4.5} \end{gathered}`

Step 4

Substitute t = 4.5 into the height equation.

`\begin{gathered} h\text{ = -16 }*\text{ 4.5}^2\text{ + 144 }*\text{ 4.5} \\ h\text{ = -324 + 648} \\ \text{h = 324} \end{gathered}`