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 83ft2 traveling at 20mph experiences a drag force of 996 N . find the drag force of a boat having a wet surface area of 125 ft2 and traveling 18 mph

We're told from the question that 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, this can be expressed mathematically as;

[tex]\begin{gathered} F\propto As^2 \\ F=kAs^2 \end{gathered}[/tex]

where k = constant of proportionality

Given A = 83 ft^2

s = 20 mph

F = 996N

Let's go ahead and substitute these values into the above equation and solve for k;

[tex]\begin{gathered} 996=k\times83\times20^2 \\ 996=33200k \\ k=\frac{996}{33200}=0.03 \end{gathered}[/tex]

Given A = 125 ft^2, s = 18 mph and we know that k = 0.03, let's go ahead and solve for F;

[tex]\begin{gathered} F=0.03\times125\times18^2 \\ F=1215N \end{gathered}[/tex]