Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 3 - Vectors and Coordinate Systems - Exercises and Problems: 41

Answer

The ducks should fly at angle of $41.4^{\circ}$ south of west.

Work Step by Step

The relative velocity of the ducks with respect to the ground $v_{dg}$ is equal to the sum of the velocity of the ducks with respect to the air $v_{da}$ and the velocity of the air with respect to the ground $v_{ag}$. The east-west component of $v_{dg}$ is zero. Let $\theta$ be the angle that is south of west that the ducks should fly. Therefore: $v_{dg,x}= v_{da,x}+v_{ag,x} = 0$ $v_{da,x}= -v_{ag,x}$ $-(8.0~m/s)~cos(\theta) = -6.0~m/s$ $\theta = arccos(\frac{6.0}{8.0})$ $\theta = 41.4^{\circ}$ The ducks should fly at angle of $41.4^{\circ}$ south of west.
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