Airplane Velocity: Calculating Speed and Heading

[anuurcc]

Homework Statement

You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 32 m/s at an angle of 30° west of due north.

Homework Equations

1)What is the speed of the plane with respect to the ground?
2)What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east).
3)How far east will the plane travel in 1 hour?

The Attempt at a Solution

I tried to set up the problem but can't visualize the vectors with respect to the wind angle given. Any help would be appreciated!

 

[Spinnor]

Draw pictures! %^), simple at first.

Suppose the plane heads north at 100mph but flies into a wind going 50mph? What is the speed relative to ground? You could do that in your head but draw the picture and the vectors. You add the vectors to get a resultant vector which is the velocity relative to the ground.

Suppose the plane again heads north at 100mph but there is a wind from the east at 100 mph. Add the vectors to get the resultant. The plane in this case travels north west at a speed of sqrt(2)*100

Still confused? Is your textbook of little help, see:

http://www.physicsclassroom.com/class/vectors/u3l1f.cfm