Finding the Direction of an Airplane Given Airspeed and Cross Wind Velocity

[vincitveritas]

Homework Statement

An airplane is flying at an airspeed of 620 km/hr in a cross wind that is blowing from the northeast at a speed of 50km/hr. In what direction should the plane head to end up going due east?

Homework Equations

v+w=(xi+yj), trig identities

The Attempt at a Solution

I think the j component is equal to 25sqrt(2) but I don't understand where the airspeed fits into finding the direction the plane should head.

 

[HallsofIvy]

The airspeed is, of course, the "length" of the velocity vector. I suggest that you draw the windspeed vector as a line of "length" 50 at angle 45 degrees to the vertical (NE). Draw from the base of that vector a horizontal ray (due East) representing the velocity you want the airplane to make- a ray rather than a vector of line segment because you do not know the "length". Geometrically, if you use compasses to strike a circle of radius from the base of the "windspeed" vector of length 620, representing the airspeed, it will intersect that line where true velocity vector is. It may intersect in two different points. Look carefully at the triangles formed. I suspect you will need to use the cosine law or sine law to find the angle you want.