# Math Help - relative velocity (physics question)

1. ## relative velocity (physics question)

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?

2. Hello,

I can give you a hint:

The plane is flying 300km/h 30deg west of south. It's vertical component (in the southern direction) of its ground velocity is thus 300cos(30).

Let me know if you are still struggling.

3. You have $\mathbf{v}_{\textrm{ground}}=-300\sin{30^\circ}\mathbf{i}-300\cos{30^\circ}\mathbf{j}=-150(\mathbf{i}+\sqrt{3}\mathbf{j})$.

The wind velocity is $\mathbf{w}=-150\mathbf{j}$.

Now use the equation $\mathbf{v}_{\textrm{air}}+\mathbf{w}=\mathbf{v}_{\ textrm{ground}}$ and solve for $\mathbf{v}_{\textrm{air}}$.