Question

Work: A set of fireworks mortar shells is launched from the staging platform at 100 ft/secfrom an initial height of eight feet above the ground. The height of the fireworks h(t), canbe modeled by, h(t) = -16t2 + 100t + 8, where t is the time in seconds after launch.

Answer 1

the maximum height and the second where that happens is the vertex

the vertex of a parabola can be solved using:

$\begin{gathered} \text{t}_{vertex}=\frac{-b}{2a} \\ a=-16 \\ b=100 \\ c=8 \end{gathered}$$t_{vertex}=-\frac{100}{2\cdot(-16)}=3.125$$\begin{gathered} h(t_{vertex})=-16\cdot(3.125)^2+100\cdot(3.125)+8 \\ h(t_{vertex})=-156.25+312.5+8=164.25 \end{gathered}$

so the answer is:

the maximum height is: 164.25 ft

and the time when that happens is 3.125 s after launch