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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?

Question 5Points 3A Model Rocket Is Projected Straight Upward From The Ground Level According To Theheight Equation H 16f2 144t Tgt 0 Where H Is The Height In F class=

Sagot :

Solution

Step 1:

Write the equation:

[tex]h\text{ = -16t}^2\text{ + 144t}[/tex]

Step 2

[tex]At\text{ maximum height, }\frac{dh}{dt}\text{ = 0}[/tex]

Step 3:

[tex]\begin{gathered} h\text{ = -16t}^2\text{ + 144t} \\ \\ \frac{dh}{dt}\text{ = -32t + 144} \\ \\ 32t\text{ = 144} \\ t\text{ = }\frac{144}{32} \\ t\text{ = 4.5} \end{gathered}[/tex]

Step 4

Substitute t = 4.5 into the height equation.

[tex]\begin{gathered} h\text{ = -16 }\times\text{ 4.5}^2\text{ + 144 }\times\text{ 4.5} \\ h\text{ = -324 + 648} \\ \text{h = 324} \end{gathered}[/tex]

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