Question

an observation deck extends 199 feet out above a valley. the deck sits 149 feet above the valley floor. if an object is dropped from the observation deck, its height h in feet, after t seconds, is given by h = -16t² + 149. how long will it take for the object to be 5 feet above the valley floor? it will take \square seconds for the object to be 5 feet above the valley floor. (type an integer or a decimal)

Explanation:

Step1: Set up the equation

We know the height formula \( h = -16t^2 + 149 \), and we want to find \( t \) when \( h = 5 \). So we set up the equation:
\( 5=-16t^{2}+149 \)

Step2: Solve for \( t^2 \)

Subtract 149 from both sides:
\( 5 - 149=-16t^{2} \)
\( - 144=-16t^{2} \)
Divide both sides by - 16:
\( t^{2}=\frac{-144}{-16} = 9 \)

Step3: Solve for \( t \)

Take the square root of both sides. Since time \( t\geq0 \) (we are dealing with time after the object is dropped), we consider the positive square root:
\( t=\sqrt{9}=3 \)

Answer:

3