Jet & Wind Vectors

Application of vectors in navigation

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