Calculating Wind Velocity: Solving for Magnitude and Direction

[Chocolaty]

I just can't figure out how to determine the magnitude and direction of the wind's velocity with this information, the combinasons of possibilities seem endless.

An airplane traveling at a cruising velocity of 1000 km/h is headed south toward a destination of 1500 km away. In order to maintain its southward heading, the airplane must travel on a course [S15°W].

Determine the magnitude and direction of the wind's velocity.

Thanks in advance

 

[z-component]

Hint: Try drawing a diagram of the velocity vectors on a coordinate system to visualize what's going on.

 

[Chocolaty]

I'm coming up with 261 km/h [E7,5°S]

I'm not too sure about this answer though, can anyone tell me if I'm right or not?

 

[mathmike]

add two of the vectors and see if you come up with the third

 

[Novolks]

I'm not too sure why they give you the 1500km away, unless there's more to the question. I'm sorry if my diagram is rudimentary.