College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 3 - Problems - Page 116: 84


(a) The plane must head at an angle of $76.4^{\circ}$ north of east. (b) The flight takes 2.72 hours.

Work Step by Step

(a) In order to travel directly north, the east component of the plane's airspeed must be equal in magnitude to the west component of the wind's speed. Let $\theta$ be the angle north of east at which the plane heads. We can find the angle $\theta$: $(300.0~km/h)~cos~\theta = (100.0~km/h)~cos~45^{\circ}$ $cos~\theta = \frac{(100.0~km/h)~cos~45^{\circ}}{300.0~km/h}$ $\theta = cos^{-1}(\frac{(100.0~km/h)~cos~45^{\circ}}{300.0~km/h})$ $\theta = 76.4^{\circ}$ To travel directly north, the plane must head at an angle of $76.4^{\circ}$ north of east. (b) We can find the north component of the plane's groundspeed: $v_y = (300.0~km/h)~sin~76.4^{\circ} - (100.0~km/h)~sin~45^{\circ}$ $v_y = 220.88~km/h$ We can find the time it takes to fly 600.0 km north: $t = \frac{d}{v_y} = \frac{600.0~km}{220.88~km/h} = 2.72~h$ The flight takes 2.72 hours.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.