Vectors in the Plane

[KingZora]

An airplane pilot whose craft has an air speed of 150 km/h wishes to fly on a true course of 65 degrees. A 15 km/h wind is blowing with a bearing of 135 degrees.

In what direction should the plane be pointed?

What will be the plane's ground speed?

 

[Ishuda]

An airplane pilot whose craft has an air speed of 150 km/h wishes to fly on a true course of 65 degrees. A 15 km/h wind is blowing with a bearing of 135 degrees.

In what direction should the plane be pointed?

What will be the plane's ground speed?

Is the 15 km/hr wind a true or relative bearing of 135 degrees?

 

[HallsofIvy]

Assuming the "135 degrees" is a true bearing, draw a picture. Draw one line segment with angle (with "north", i.e. vertical) 65 degrees and length 150. Draw a second line segment with same base point, with angle 135 degrees and length 15. You want a vector that, added to the wind vector, will give the desired path. That will be the line segment from the end of the wind vector to the end of the desired path vector.

Do you see now that you have a triangle with one side of length 150 and the other of length 15? And it is easy to find the angle between those lines. So you can use the "cosine law" to find the length of the opposite side.