Example: A jet airliner, flying due east at 800 km/hr in still air, encounters a 250-km/hr tailwind blowing in the direction 60 degrees north of east. The airplane holds its compass heading due east but, because of the wind, acquires a new ground speed and direction. What are they?

Solution: If u = the velocity of the airplane alone and v = the velocity of the tailwind, then |u|=800 and |v|=250. The velocity of the airplane with respect to the round is given by the magnitude and direction of the resultant vector u+v.
If we let the positive x-axis represent east and the positive y-axis represent north, then the component forms of u and v are:
u=<800,0> and v=<250 cos 60, 250 sin 60>
We can obtain different values for vectors u and v, and different values for the angle, if we move the slider or enter another values for u and v!