Q. 8.132 - Intermediate Algebra

Question

A window washer dropped a squeegee from a platform $196$ feet above the sidewalk Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the squeegee to reach the sidewalk. 

Step-by-Step Solution

Answer

It will take $3.5$ seconds for the squeegee to reach the sidewalk. 

Step 1. Identify and name what we are looking for

It is given that the squeegee is dropped from a height of $196$ 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 $196$ feet. So the equation is

$h=196 ...\left(1\right)$

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 $196$ for $h$ in the second equation and solve for $t$.

$$\begin{gathered} t=\frac{\sqrt{h}}{4} \\ t=\frac{\sqrt{196}}{4} \\ t=\frac{14}{4} \\ t=3.5 \end{gathered}$$

Step 4. Check the solution

Substitute $3.5$ for $t$ and $196$ for $h$ in the second equation.

$\begin{array}{rcl}t& =& \frac{\sqrt{h}}{4}\\ 3.5& =& \frac{\sqrt{196}}{4}\\ 3.5& =& \frac{14}{4}\\ 3.5& =& 3.5\end{array}$

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