Q. 8.131 - Intermediate Algebra

Question

A helicopter dropped a rescue package from a height of $1,296$ feet. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground. 

Step-by-Step Solution

Answer

It will take $9$ seconds for the package to reach the ground.

Step 1. Identify and name what we are looking for

It is given that the package is dropped from a height of $1296$ feet.

The objective is to find the time it will take to reach the ground.

So let $t$ represents the required time.

Step 2. Form the equations

The height is $1296$ feet. So the equation is

$h=1296 ...\left(1\right)$

And the formula is given by the equation  $t=\frac{\sqrt{h}}{4} ...\left(2\right)$

Step 3. Solve using substitution

Using the first equation substitute $1296$ for $h$ in the second equation and solve for $t$.

$\begin{array}{rcl}t& =& \frac{\sqrt{h}}{4}\\ t& =& \frac{\sqrt{1296}}{4}\\ t& =& \frac{36}{4}\\ t& =& 9\end{array}$

Step 4. Check the solution

Substitute $9$ for $t$ and $1296$ for $h$ in the second equation.

$$\begin{gathered} t=\frac{\sqrt{h}}{4} \\ 9=\frac{\sqrt{1296}}{4} \\ 9=\frac{36}{4} \\ 9=9 \end{gathered}$$

As the statement is true, so the found solution is correct.