Question

A toy rocket is shot vertically into the air from a launching pad 6 feel above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground as t seconds after launch is given by the function h(t)=-16t^2+40t+6. How long will it take the rocket to reach its maximum height? What is the maximum height? CAN ANYONE HELP ME ASAP!!!! Thank you in advance

Answer 1

Check the picture below.

so let's simply check about what's its vertex then

`\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+40}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)`

`\left(-\cfrac{ 40}{2(-16)}~~~~ ,~~~~ 6-\cfrac{ (40)^2}{4(-16)}\right) \implies \left( - \cfrac{ 40 }{ -32 }~~,~~6 - \cfrac{ 1600 }{ -64 } \right) \\\\\\ \left( \cfrac{ -5 }{ -4 } ~~~~ ,~~~~ 6 +25 \right)\implies {\Large \begin{array}{llll} \stackrel{ ~~ seconds~\hfill feet ~~ }{\left( ~~ 1(1)/(4)~~ ~~ , ~~ ~~31 ~~ \right)} \end{array}}`