analyze the graph of a cannon - ball launched from the ground with an initial velocity of 144 feet per…

analyze the graph of a cannon - ball launched from the ground with an initial velocity of 144 feet per second. the cannon - ball reached its maximum height after 4.5 seconds. what was the maximum height the cannon - ball reached? feet

analyze the graph of a cannon - ball launched from the ground with an initial velocity of 144 feet per second. the cannon - ball reached its maximum height after 4.5 seconds. what was the maximum height the cannon - ball reached? feet

Answer

Explanation:

Step1: Substitute time into height - formula

We know the height - time function $h(t)=-16t^{2}+144t$, and the time $t = 4.5$ seconds when the cannon - ball reaches its maximum height.

Step2: Calculate the maximum height

Substitute $t = 4.5$ into $h(t)$: [ \begin{align*} h(4.5)&=-16\times(4.5)^{2}+144\times4.5\ &=-16\times20.25 + 648\ &=-324+648\ &=324 \end{align*} ]

Answer:

324