Determining Wind Velocity From Light Plane Flight

[mikenash]

A light plane attains an airspeed of 470 km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 17.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude (in km/h) and (b) direction of the wind velocity? Give the direction as an angle relative to due west, where north of west is a positive angle, and south of west is a negative angle.

Pyj-800j=wj
Pxi=Wxi

attempt

tan inverse
(wx/WY)

then i got lost and do not know how to start the problem

 

[Andrew Mason]

A light plane attains an airspeed of 470 km/h. The pilot sets out for a destination 800 km due north but discovers that the plane must be headed 17.0° east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude (in km/h) and (b) direction of the wind velocity? Give the direction as an angle relative to due west, where north of west is a positive angle, and south of west is a negative angle.

Pyj-800j=wj
Pxi=Wxi

attempt

tan inverse
(wx/WY)

then i got lost and do not know how to start the problem

Draw a vector diagram. One vector $\vec v_{pa}$ represents the velocity of the plane relative to the air. The other vector $\vec v_{ag}$ represents the velocity of the air relative to the ground. What does the resultant vector ($\vec v_{pa}+\vec v_{ag} = \vec v_{pg}$ represent? (Hint: I have given you a hint). Do we know the length of this vector? Do we know the length of $\vec v_{pa}$? Do we know its angle relative to $\vec v_{pg}$? Resolve the North and West components of $\vec v_{pa}$. What do these components plus the North and West components of $\vec v_{ag}$ have to add up to?

AM