Vector equation help: Find Wind Velocity Vector

[Zanesco]

Homework Statement

An airplane flies at an airspeed of 459 km/hr. The pilot wants to fly 784 km to the north. She knows that she must head 21.6° east of north to fly directly there. If the plane arrives in 2.07 hr, find the magnitude of the wind velocity vector.

Tried solving as seen below but I'm not sure where I'm going wrong.

Homework Equations

The Attempt at a Solution

v=d/t
459 km/h=d/2.07 h
950.13 km=d

srt(950.13^2-784^2)=b
66.05 km=b

v=66.05 km/2.07 h
v=31.9 km/h

 

[Astronuc]

Homework Statement

An airplane flies at an airspeed of 459 km/hr. The pilot wants to fly 784 km to the north. She knows that she must head 21.6° east of north to fly directly there. If the plane arrives in 2.07 hr, find the magnitude of the wind velocity vector.

Tried solving as seen below but I'm not sure where I'm going wrong.

Homework Equations

The Attempt at a Solution

v=d/t
459 km/h=d/2.07 h
950.13 km=d

srt(950.13^2-784^2)=b
66.05 km=b

v=66.05 km/2.07 h
v=31.9 km/h

The plane flies in the air at a speed of 459 km/h for 2.07 hrs, so the distance is correct. However, the plane flies at an angle of 21.6 deg E of N. What is the projection from the planes trajectory in the air on to due north?

 

[Zanesco]

it would be: 459cos21.6=426.77 km/h