Relative Velocity Problem: What is the True Velocity of the Wind?

[binbagsss]

When a women cycles N at 40kmh^-1, the wind appears to be blowing from a E direction, however when she cycles S at 50kmh^-1, the wind appears to be blowing from the SE.

Find the true velocity of the wind.

My attempt is attached - I have tried to solve through components and usingthe fact that the direction that the wind appears is known each time to establish an angle relationship with the components.

The only trouble is I am unsure what to set tan x when the direction is purely East.

Thanks alot.

 

[tms]

The first part tells you the N-S component of the wind since the cyclist is at rest with respect to the wind. From that, you should be able to get the E-W component from the second part.