we are standing on the top of a 304 feet tall building and launch a small object upward. the objects…

we are standing on the top of a 304 feet tall building and launch a small object upward. the objects vertical position, measured in feet, after t seconds is h(t)= - 16t² + 288t + 304. what is the highest point that the object reaches? feet question help: message instructor submit question

we are standing on the top of a 304 feet tall building and launch a small object upward. the objects vertical position, measured in feet, after t seconds is h(t)= - 16t² + 288t + 304. what is the highest point that the object reaches? feet question help: message instructor submit question

Answer

Explanation:

Step1: Find the time of maximum height

The function $h(t)= - 16t^{2}+288t + 304$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-16$, $b = 288$, $c = 304$. The time $t$ at which the object reaches its maximum height is given by the formula $t=-\frac{b}{2a}$. $t=-\frac{288}{2\times(-16)}=\frac{288}{32} = 9$.

Step2: Calculate the maximum height

Substitute $t = 9$ into the height - function $h(t)$. $h(9)=-16\times9^{2}+288\times9 + 304$. First, calculate $-16\times9^{2}=-16\times81=-1296$. Then, calculate $288\times9 = 2592$. $h(9)=-1296+2592 + 304$. $h(9)=1296+304=1600$.

Answer:

1600