A light plane attains an airspeed of 500 km/h. The pilot sets out for a destination 900 km due north but discovers that the plane must be headed `20.0^(@)` east of due north to fly there directly. The plane arrives in 2.00 h. What were the (a) magnitude and (b) direction of the wind velocity?

Explanation

To solve the problem, we need to find the wind velocity based on the information given about the plane's airspeed, heading, and travel time. Let's break it down step by step.

### Step 1: Determine the plane's velocity vector
The plane's airspeed is given as 500 km/h. The pilot heads 20 degrees east of due north. We can break this velocity into its components:

- The northward (y) component:
\[
V_{py} = V_p \cdot \cos(20^\circ) = 500 \cdot \cos(20^\circ)
...