Question

a ball is dropped from a 30 - foot - tall building, meaning it has no initial velocity. write a model h(t) that represents the height of the ball from the ground, in feet, t seconds after it is dropped from the building. (2 points)
h(t)=□t²+□t+□

Explanation:

Step1: Recall the free - fall formula

The general formula for the height of an object in free - fall 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. In the English system of units, $g = 32\ ft/s^2$.

Step2: Identify the initial conditions

The ball is dropped from a 30 - foot - tall building, so $h_0=30$ feet. It has no initial velocity, so $v_0 = 0\ ft/s$.

Step3: Substitute the values into the formula

Substitute $h_0 = 30$, $v_0=0$, and $g = 32$ into $h(t)=h_0 + v_0t-\frac{1}{2}gt^2$. We get $h(t)=30+0\times t-\frac{1}{2}\times32t^2$.

Step4: Simplify the formula

$h(t)=30 - 16t^2$, which can be written in the form $h(t)=- 16t^2+0t + 30$.

Answer:

$h(t)=-16t^2 + 0t+30$