College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 60

According to physics, the maximum range $R$ of a projectile is directly proportional to the square of its velocity $\nu$. A baseball pitcher throws a ball at $60 \frac{\text{mi}}{\text{h}}$, with a maximum range of $242 \text{ft}$. What is his maximum range if he throws the ball at $70 \frac{\text{mi}}{\text{h}}$

$\begin{equation} \begin{aligned} R_1 &= k (\nu_1)^2\\ \\ k &= \frac{R_1}{(\nu_1)^2} && \Longleftarrow\text{Equation 1} \end{aligned} \end{equation}$


$\begin{equation} \begin{aligned} R_2 &= k (\nu_2)^2\\ \\ k &= \frac{R_2}{(\nu_2)^2} && \Longleftarrow\text{Equation 2} \end{aligned} \end{equation}$


Using Equations 1 and 2

$\begin{equation} \begin{aligned} \frac{R_1}{(\nu_1)^2} & = \frac{R_2}{(\nu_2)^2} && \text{Apply cross multiplication}\\ \\ R_2 (\nu_1)^2 &= R_1 (\nu_2)^2 && \text{Solve for } R_2\\ \\ R_2 &= \left( \frac{\nu_2}{\nu_1} \right)^2 R_1 && \text{Substitute the given}\\ \\ R_2 &= \left( \frac{70}{60} \right)^2 (242 \text{ ft})\\ \\ R_2 &= 329.38 \text{ or } 329 \text{ ft} \end{aligned} \end{equation}$