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 134 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 $S=134$, we substitute $S$ into the formula: $134 = 16t^{2}$.

Step2: Solve for $t^{2}$

Divide both sides of the equation by 16: $t^{2}=\frac{134}{16}=\frac{67}{8}= 8.375$.

Step3: Solve for $t$

Take the square - root of both sides. Since $t$ represents time and cannot be negative in this context, $t=\sqrt{8.375}\approx2.9$.

Answer:

$2.9$