Mathematics, 15.07.2019 14:00, khaylaperry
Using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. interpret what the value represents in this situation.
Answers: 1
![h=-16t^2+v_{0}t+h_{0}\\\\h=-16(t^2-\frac{v_{0}t}{16}-\frac{h_{0}}{16})\\\\h=-16[(t-\frac{v_{0}}{32})^2-(\frac{v_{0}}{32})^2-\frac{h_{0}}{16}]\\\\h-16[(\frac{v_{0}}{32})^2+\frac{h_{0}}{16}]=-16[(t-\frac{v_{0}}{32})]^2\\\\ \text{This is a function in t and h}\\\\ \text{Vertex}=(\frac{v_{0}}{32},16[(\frac{v_{0}}{32})^2+\frac{h_{0}}{16})])](/tpl/images/0092/7389/e7750.png)
![h=-16t^2+v_{0}t+h_{0}\\\\\frac{dh}{dt}=-32 t+v_{0}\\\\\text{Put},\frac{dh}{dt}=0\\\\\rightarrow -32 t+v_{0}=0\\\\\rightarrow t=\frac{v_{0}}{32}\\\\\text{Extreme value}=-16*[\frac{v_{0}}{32}]^2+v_{0}*\frac{v_{0}}{32}+h_{0}\\\\f(t)=-16*[\frac{v_{0}}{32}]^2+\frac{(v_{0})^2}{32}+h_{0}\\\\\frac{d^2h}{dt^2}=-32\\\\\text{Showing that function attains maximum at this point}](/tpl/images/0092/7389/3407b.png)
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Using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically det...
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