SOLUTION: An airplane maintains a speed with respect to the air in the absence of wind of 280 mi/h and is on a bearing of N 40° W. If the wind is blowing west at 30 mi/h, determine the fina

Question 1168004: An airplane maintains a speed with respect to the air in the absence of wind of 280 mi/h and is on a bearing of N 40° W. If the wind is blowing west at 30 mi/h, determine the final bearing of the airplane and its speed with respect to the earth. (300 mph, N 44° W)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
An airplane maintains a speed with respect to the air in the absence of wind of 280 mi/h and is on a bearing of N 40° W. If the wind is blowing west at 30 mi/h, determine the final bearing of the airplane and its speed with respect to the earth. (300 mph, N 44° W)
===================================
An airplane maintains an airspeed of 280 mi/h and is on a bearing of 320°. If the wind is from 270 at 30 mi/h, determine the ground track of the airplane and its groundspeed. (300 mph, N 44° W)
-----
Use the cosine Law
2 sides and the included angle are given.
g^2 = 280^2 + 30^2 - 2*280*30*cos(40)
g =~ 257.74 mi/hr
----
Use the Law of Sines to find the small angle
257.74/sin(40) = 30/sin(A)
sin(A) = 4.29 degs
Ground track = 324.29 degs
======================
Wind is always given as direction it's FROM.
If you meant it was from the east ("blowing west") you'll have to rework it using the same methods.
RELATED QUESTIONS
If the speed of an airplane is 350 mi/h with a tail wind of 40 mi/h what is the speed of... (answered by TimothyLamb)

An airplane flies 738 mi against the wind and 1062 mi with the wind in a total time of 9... (answered by checkley77)

A pool can be filled by one particular pipe in 10h, whereas a different pipe requires 6 h (answered by edjones)

A certain airplane can maintain a speed, without the presence of wind, of 210 mi/h and... (answered by CPhill,ikleyn)

An airplane flies 738 miles against the wind & 1062 miles with the wind in a total time... (answered by jorel1380)

An airplane flies 1449 mi against the wind and 1539 mi with the wind in a total time of... (answered by josmiceli)

need a system of equations for this prob: an airplane flew 4 hours against a wind of 40... (answered by funmath)

An airplane is headed 123 degrees with an air speed of 310 mph with a wind of 40 mph on a (answered by stanbon)

The speed of an airplane in still air is 248 mph. The plane travels 816 mi agains the... (answered by josmiceli)