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 $72 \mathrm{ft}^{2}$ traveling at $12.5 \mathrm{mph}$ experiences a drag force of $675 \mathrm{~N}$. Find the speed of a boat experiencing a drag force of $384 \mathrm{~N}$ and having a wet surface area of $25 \mathrm{ft}^{2}$.

Step 1 ：Given 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, we can represent this relationship with the equation $F = kAs^2$, where $k$ is the constant of variation.

Step 2 ：We are given that a boat with a wet surface area of $72 \mathrm{ft}^{2}$ traveling at $12.5 \mathrm{mph}$ experiences a drag force of $675 \mathrm{~N}$. We can substitute these values into the equation to find the value of $k$.

Step 3 ：\[k = \frac{F}{As^2} = \frac{675}{72 \times (12.5)^2} = 0.06\]

Step 4 ：Now we can use the value of $k$ to find the speed $s$ of a boat experiencing a drag force of $384 \mathrm{~N}$ and having a wet surface area of $25 \mathrm{ft}^{2}$. We substitute these values into the equation and solve for $s$.

Step 5 ：\[s = \sqrt{\frac{F}{kA}} = \sqrt{\frac{384}{0.06 \times 25}} = 16.0\]

Step 6 ：\(\boxed{16.0 \mathrm{~mph}}\) is the speed of a boat experiencing a drag force of $384 \mathrm{~N}$ and having a wet surface area of $25 \mathrm{ft}^{2}$.