relative velocity (physics question)

**checkmarks** · March 4th 2008, 04:14 PM

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?

**sandstorm** · March 5th 2008, 04:02 AM

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.

**JaneBennet** · March 5th 2008, 06:16 AM

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 $\mathbf{v}_{\textrm{air}}$ .

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