Question

An airplanes velocity with respect to the air is 580 miles per hour, and it is heading N60 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?

Answer 1

The resultant speed can be found using the cosine rule:
\[c ^{2}=a ^{2}+b ^{2}-2ab \cos C=580^{2}+60^{2}-2(580\times 60\times \cos 75)\]
c = 567.4 miles per hour ground speed
Can you work out the true direction now?