the height h of a fireball launched from a roman candle with an initial velocity of 64 feet per second is…
the height h of a fireball launched from a roman candle with an initial velocity of 64 feet per second is given by the equation h = - 16t² + 64t, where t is time in seconds after launch. use the graph of this function to answer the questions.\na) estimate the maximum height of the fireball.\nthe maximum height of the fireball is ft.
Answer
Explanation:
Step1: Identify the function type
The height - function $h(t)=-16t^{2}+64t$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 64$, and $c = 0$.
Step2: Find the time of maximum height
For a quadratic function $y = ax^{2}+bx + c$, the $x$ - coordinate (in our case, the time $t$) of the vertex is given by $t=-\frac{b}{2a}$. Substituting $a=-16$ and $b = 64$ into the formula, we have $t=-\frac{64}{2\times(-16)}=\frac{-64}{-32}=2$.
Step3: Calculate the maximum height
Substitute $t = 2$ into the height - function $h(t)=-16t^{2}+64t$. Then $h(2)=-16\times2^{2}+64\times2=-16\times4 + 128=-64 + 128 = 64$.
Answer:
64