Question

the formula s = 16t^2 is used to approximate the distance s, in feet, that an object falls freely from rest in t seconds. the height of a building is 1354 feet. how long would it take for an object to fall from the top? the object would fall for seconds. (simplify your answer. type an integer or a decimal rounded to the nearest tenth.)

Explanation:

Step1: Set up the equation

Given $S = 16t^{2}$ and $S=1354$, we have $16t^{2}=1354$.

Step2: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{1354}{16}=\frac{677}{8}=84.625$.

Step3: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative, $t=\sqrt{84.625}\approx9.2$.

Answer:

$9.2$