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)
$h(t)=square t^{2}+square t+square$
check answer remaining attempts : 3

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.

Step2: Identify the given values

We know that the ball is dropped from a 30 - foot - tall building, so $h_0 = 30$. The initial velocity $v_0 = 0$ (since it is just dropped). The acceleration due to gravity $g = 32$ ft/s² in English units.

Step3: Substitute values into the formula

Substituting $h_0 = 30$, $v_0 = 0$, 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 as $h(t)=- 16t^2+0t + 30$.

Answer:

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