Answer
$72$ ergs
Work Step by Step
Solving Variation Problems (see p. 424)
1. $\ \ $Write an equation that models the given English statement.
2. $\ \ $Substitute the given pair of values into the equation in step 1 and find the value of k, the constant of variation.
3. $\ \ $Substitute the value of k into the equation in step 1.
4. $\ \ $Use the equation from step 3 to answer the problem's question.
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1.
Let $E_{k}$ be the kinetic energy (ergs),
m the mass (grams)
v the velocity (cm/s),
$E_{k}$ varies jointly (directly) as $m$ and $v^{2},\ \qquad E_{k}=kmv^{2}$
2.
$36=k(8)(3^{2})$
$36=k(72)\qquad /\div 72$
$k=\displaystyle \frac{36}{72}=\frac{1}{2}=0.5$
3.
$E_{k}=\displaystyle \frac{1}{2}mv^{2}$
4
$m=4, v=6, E_{k}=?$
$E_{k}=\displaystyle \frac{1}{2}(4)(6^{2})=72$ ergs
