Question

an observation deck extends 313 feet out above a valley. the deck sits 263 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 + 263. how long will it take for the object to be 7 feet above the valley floor? it will take seconds for the object to be 7 feet above the valley floor. (type an integer or a decimal.)

Explanation:

Step1: Set up the equation

We are given the height - time formula $h=-16t^{2}+263$, and we want to find $t$ when $h = 7$. So we set up the equation $7=-16t^{2}+263$.

Step2: Rearrange the equation

Subtract 263 from both sides: $7 - 263=-16t^{2}$, which simplifies to $-256=-16t^{2}$.

Step3: Solve for $t^{2}$

Divide both sides by - 16: $\frac{-256}{-16}=t^{2}$, so $t^{2}=16$.

Step4: Solve for $t$

Take the square - root of both sides. Since $t$ represents time, we consider the positive square root. So $t = 4$.

Answer:

4