Question

An observation deck extends 457 feet out above a valley. The deck sits 407 feet above the valley floor. If an object is dropped from the observation deck, its heighth in feet, after t seconds, is given by h= - - 161² + 2 +407. How long will it take for the object to be 7 feet above the valley floor? It will take 4.13 seconds for the object to be 7 feet above the valley floor (Type an integer or a decimal)

Answer 1

The height equation:

$h=-16t^2+407$

We want to know how long it will take [t] for the object to be 7 feet above the floor.

So, we substitute 7 into h and solve the equation for t. Shown below:

$\begin{gathered} 7=-16t^2+407 \\ 16t^2=407-7 \\ 16t^2=400 \\ t^2=\frac{400}{16} \\ t^2=25 \\ t=\sqrt[]{25} \\ t=5 \end{gathered}$

Thus, after t = 5 seconds, the height of the object is 7 feet above valley floor.