Question

the formula s = 16t² 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 1185 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: Substitute S value into formula

Given $S = 16t^{2}$ and $S=1185$, we get $1185 = 16t^{2}$.

Step2: Solve for $t^{2}$

Divide both sides by 16: $t^{2}=\frac{1185}{16}=74.0625$.

Step3: Solve for t

Take the square - root of both sides. Since $t>0$ (time cannot be negative in this context), $t=\sqrt{74.0625}\approx8.6$.

Answer:

$8.6$