Answer: [tex]53.31\°[/tex] East of North
Explanation:
We have the following data:
Speed of the wind from East to West: [tex]6.68 m/s[/tex]
Speed of the bee relative to the air: [tex]8.33 m/s[/tex]
If we graph these speeds (which in fact are velocities because are vectors) in a vector diagram, we will have a right triangle in which the airspeed of the bee (its speed relative to te air) is the hypotense and the two sides of the triangle will be the Speed of the wind from East to West (in the horintal part) and the speed due North relative to the ground (in the vertical part).
Now, we need to find the direction the bee should fly directly to the flower (due North):
[tex]sin \theta=\frac{Windspeed-from-East-to-West}{Speed-bee-relative-to-air}[/tex]
[tex]sin \theta=\frac{6.68 m/s}{8.33 m/s}[/tex]
Clearing [tex]\theta[/tex]:
[tex]\theta=sin^{-1} (\frac{6.68 m/s}{8.33 m/s})[/tex]
[tex]\theta=53.31\°[/tex]
