Question

an object is dropped from 33 feet below the tip of the pinnacle atop a 1189 - ft tall building. the height h of the object after t seconds is given by the equation h = - 16t² + 1156. find how many seconds pass before the object reaches the ground.
seconds pass before the object reaches the ground.
(type an integer or a decimal.)

Explanation:

Step1: Set height to 0

When the object reaches the ground, $h = 0$. So we set up the equation $0=-16t^{2}+1156$.

Step2: Rearrange the equation

Add $16t^{2}$ to both sides of the equation: $16t^{2}=1156$.

Step3: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{1156}{16}=72.25$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t\geq0$ (time cannot be negative in this context), $t=\sqrt{72.25}=8.5$.

Answer:

$8.5$