Question

The drag force F on a boat varies jointly with the wet surface area A of the boat and the square of the speed s of the boat. A boat with a wet surface area of 50ft2 traveling at 7mph experiences a drag force of 98N . Find the wet surface area of a boat traveling 7.5mph and experiencing a drag force of 135N .

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{cases} F=\textit{drag force}\\ w=\textit{wet area}\\ s=speed \end{cases}\textit{\underline{F} varies jointly with \underline{w} and square of \underline{s}}\quad F=kws^2$

$\bf \textit{we also know that } \begin{cases} w=502\\ F=98\\ s=7 \end{cases}\implies 98=k502\cdot 7^2 \\\\\\ 98=24598k \implies \cfrac{98}{24598}=k\implies \cfrac{1}{251}=k\qquad \implies \boxed{F=\cfrac{1}{251}ws^2}\\\\ -------------------------------\\\\ \textit{now, what's \underline{w} when } \begin{cases} s=7.5\\ F=135 \end{cases}\implies 135=\cfrac{1}{251}w7.5^2 \\\\\\ \cfrac{135\cdot 251}{56.25}=w\implies 604.2=w$