Question

the function h(t)=-16t^{2}+32t + 24 represents the height of an object t seconds after being launched straight into the air. what does - 16 represent?
initial velocity
time until the object hits the ground
acceleration due to gravity
maximum height

Explanation:

Step1: Recall the height - time formula

The general formula for the height of an object in vertical - motion under the influence of gravity (neglecting air resistance) is $h(t)=h_0 + v_0t-\frac{1}{2}gt^2$, where $h_0$ is the initial height, $v_0$ is the initial velocity, and $g$ is the acceleration due to gravity.

Step2: Compare with the given function

The given function is $h(t)=- 16t^2+32t + 24$. Comparing it with $h(t)=h_0 + v_0t-\frac{1}{2}gt^2$, we have $-\frac{1}{2}g=-16$. Solving for $g$ gives $g = 32$. In the English system of units, the acceleration due to gravity $g$ is approximately $32\ ft/s^2$. So, the coefficient $-16$ in the function $h(t)$ represents $-\frac{1}{2}g$, which is related to the acceleration due to gravity.

Answer:

acceleration due to gravity