Question

An airplane's velocity with respect to the air is 580 miles per hour, and it is heading N 60 degrees W. The wind, at the altitude of the plane, is from the southwest and has a velocity of 60 miles per hour. Draw a figure that gives a visual representation of the problem. What is the true direction of the plane, and what is its speed with respect to the ground?

guys i have absolutely no idea on how to work on this... HELP

Answer 1

The resultant factor is <-459.9, 332.4>

I am not sure how to go about finding the magnitude and the direction from this point.

Answer 2

use law of cosines to find new speed
then use law of sines to determine true direction
\[x^{2} = 580^{2}+60^{2}-2(580)(60)\cos(75)\]
x = 567.44
\[\frac{\sin \theta}{60} = \frac{\sin 75}{567.44}\]
\[\theta = 5.86\]
true direction is N 54.14 degrees W