Thread: Did I do this vector question right?

A plane is heading S 70degrees W with a groundspeed of 625km/h. If the pilot is steering west at an airspeed of 665km/h, what must be the windspeed and wind direction?

This is the diagram I drew, forgive me if the scaling is off:



The magnitude of the wind I found was:

w^2 = a^2 + g^2 -2(a)(g)(cos110degrees)

= about 1057 km/h

Is this wrong? I want to know if I have the right answer for the magnitude before attempting to find the direction of the wind.

Hello, kmjt!

Your diagram is incorrect . . .

A plane is heading S 70° W with a groundspeed of 625 km/h.
If the pilot is steering west at an airspeed of 665 km/h,
. . what must be the windspeed and wind direction?

Code:

                 665
    A o - - - - - - - - - - - o O
       \               20° *
        \               *
         \           *
          \       *  625
           \   *
            o
            B

The plane is flying from O to A at 665 km/hr.
. .

The wind is blowing from A to B.

The plane's resultant flight is: . km/hr.


Law of Cosines: .

. . Hence: .


Then: .

. . Hnce: .


Therefore, the windspeed is 227.4 km/hr and its direction is: .S 20° E.


Interesting!
Triangle ABO is virtually a right triangle . . .
.

Doh thats what I got the first time I just thought it was wrong because usually we have to calculate something to find what angle the wind is blowing at.. Thanks