Question

if a projectile is fired straight upward from the ground with an initial speed of 224 feet per second, then its height h in feet after t seconds is given by the function h(t)= - 16t² + 224t. find the maximum height of the projectile. (simplify your answer.)

Explanation:

Step1: Identify the function type

The height - function $h(t)=-16t^{2}+224t$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 224$, and $c = 0$.

Step2: Find the t - value of the vertex

For a quadratic function $y=ax^{2}+bx + c$, the $x$ - coordinate (in our case $t$ - coordinate) of the vertex is given by $t=-\frac{b}{2a}$.
So, $t=-\frac{224}{2\times(-16)}=\frac{-224}{-32}=7$.

Step3: Find the maximum height

Substitute $t = 7$ into the height - function $h(t)$.
$h(7)=-16\times7^{2}+224\times7=-16\times49 + 1568=-784+1568 = 784$.

Answer:

784