please help!!
A plane is seen to travel in a direction [S 30 degrees W]. if its ground velocity was 300 km/h and the wind speed is 150 km/h south, what is the plane's velocity relative to the air?
You have $\displaystyle \mathbf{v}_{\textrm{ground}}=-300\sin{30^\circ}\mathbf{i}-300\cos{30^\circ}\mathbf{j}=-150(\mathbf{i}+\sqrt{3}\mathbf{j})$.
The wind velocity is $\displaystyle \mathbf{w}=-150\mathbf{j}$.
Now use the equation $\displaystyle \mathbf{v}_{\textrm{air}}+\mathbf{w}=\mathbf{v}_{\ textrm{ground}}$ and solve for $\displaystyle \mathbf{v}_{\textrm{air}}$.