Correct Direction for Crossing a River A river has a constant current of $3km/hr$. At what angle to a boat dock should a motorboat capable of maintaining a constant speed of$20km/hr$ be headed in order to reach a point directly opposite the dock? If the river is $\frac{1}{2}$ kilometer wide, how long will it take to cross?

Let us consider that a river having a constant current of$3km/hr$and it is asked an angle to a boat dack, should a motorboat capable of maintaining a constant speed of$20km/hr$be headed in order to reach a point directly opposite the dock.
Further we have to determine the time also, it will take to cross the river if it is $0.5$kilometer long.

Let $S_1$represents the speed of boat in the direction of river, $S_2$represents the constant speed of river and $S_3$represents the speed of motorboat against the speed of river as shown in the above figure.

$$\begin{gathered} \sin \theta =\frac{opposite}{hypotenues} \\ =\frac{\left|S2\right|}{\left|S_1\right|} \\ =\frac{3}{20} \\ =0.15 \\ \theta ={\sin }^{-1}(0.15) \\ \approx 8.6degree \end{gathered}$$

Thus, motorboat will be at an angle of $8.6$degree, left of direct heading across the river while capable of maintaining the desire constant speed.

Again in triangle ABD,

$$\begin{gathered} \tan 8.6°=\frac{opposite}{adjacent} \\ =\frac{\left|S_2\right|}{\left|S_3\right|} \\ 0.1512=\frac{3}{S_3} \\ {S}_3=\frac{3}{0.1512} \\ {S}_3=19.8387 \end{gathered}$$