the speed of a boat in still water is 25 mph. the boat is traveling on a river with a current flowing south…

Explanation:

Step1: Set up velocity vectors

Let the velocity of the boat in still - water be $\vec{v}{b}=25$ mph and the velocity of the current be $\vec{v}{c}=10$ mph south. We want the resultant velocity to be due west. Let the angle $\theta$ be the angle the boat makes with the west - direction (upstream).

Step2: Use trigonometry

The component of the boat's velocity in the north - south direction must cancel out the velocity of the current. If the boat's velocity in still water is $v_{b} = 25$ mph, and the velocity of the current is $v_{c}=10$ mph, then $\sin\theta=\frac{v_{c}}{v_{b}}$. Substitute $v_{c} = 10$ and $v_{b}=25$ into the formula: $\sin\theta=\frac{10}{25}=0.4$.

Step3: Find the angle

To find $\theta$, we take the inverse - sine of 0.4. $\theta=\sin^{- 1}(0.4)\approx23.58^{\circ}$.

Answer:

B. $23.58^{\circ}$