Question

A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at $6.0\text{m}/\text{s}$. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at $8.0\text{m}/\text{s}$relative to the air, what direction should they head in order to move directly south?

Short answer

The correct answer is${48.6}^{°}$ east of the south

Step-by-step solution

Step 1. Given information

The speed of a duck relative to air is m/s and wind is blowing from the west with a speed of$6\text{m}/\text{s}$

Step 2. Explanation

As it is given that the speed of a duck relative to air is m/s and the wind is blowing from the west with a speed $6\text{m}/\text{s}$, so the vector diagram will be as follows, where ${\overrightarrow{v}}_w$is the velocity of wind, ${\overrightarrow{v}}_{d_w}$is the velocity of wind with respect to the wind and $v_d$is the resultant velocity.

Hence, the angle between${\overrightarrow{v_d}}_w$and $\overrightarrow{v_d},\theta$, is given as,

$\begin{array}{l}\sin \theta =\frac{v_w}{v_{wd}}\\ =\frac{6}{8}\\ \theta ={48.6}^{°}\end{array}$

Conclusion

The flock of ducks should try to fly in a direction ${48.6}^{°}$east of the south.