Respuesta :
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Define direct variation
Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k , called the constant of variation or constant of proportionality.
STEP 2: Represent the statements in mathematical terms
[tex]\begin{gathered} s\text{ varies directly as the square of t} \\ s\propto t^2 \end{gathered}[/tex]STEP 3: Express the variation in form of an equation
[tex]\begin{gathered} s\propto t^2 \\ Introducing\text{ the constant of variation, we have;} \\ s=kt^2----equation\text{ 1} \\ \\ Making\text{ k the subject of the equation, we have;} \\ Divide\text{ both sides by t}^2 \\ \frac{s}{t^2}=\frac{kt^2}{t^2} \\ k=\frac{s}{t^2}-----equation\text{ 2} \end{gathered}[/tex]STEP 4: Calculate the value of k using the given values and the equation in step 3
[tex]\begin{gathered} k=\frac{s}{t^2} \\ s=16,t=1 \\ By\text{ substitution,} \\ k=\frac{16}{1^2}=\frac{16}{1}=16 \\ \\ \therefore k=16 \end{gathered}[/tex]STEP 5: Make t the subject of the equation 1 in step 3
[tex]\begin{gathered} From\text{ equation 1 in step 3,} \\ \begin{equation*} s=kt^2 \end{equation*} \\ Make\text{ t the subject of the formula, divide both sides by k} \\ \frac{s}{k}=\frac{kt^2}{k} \\ \frac{s}{k}=t^2 \\ \\ Find\text{ the square root of both sides} \\ \sqrt{\frac{s}{k}}=\sqrt{t^2} \\ t=\sqrt{\frac{s}{k}} \end{gathered}[/tex]STEP 6: Use the derived equation in step 5 to find the value of t when s = 144
[tex]\begin{gathered} t=\sqrt{\frac{s}{k}} \\ t=\sqrt{\frac{144}{16}} \\ t=\sqrt{9} \\ t=3secs \end{gathered}[/tex]Hence, the time it takes the object to fall from 144 feet is 3 seconds
