Vector Walk in Two-Dimensions - Counter Clockwise from East Convention

A vector such as displacement has a direction associated with it. In order for such descriptions of vector quantities to be useful, it is important that everyone agree upon how the direction of a vector is described. Most of us are accustomed to the idea that up on a map refers to the northward direction and right on a map refers to the eastward direction. This is a mere convention which mapmakers have used for years and upon which we all can agree. But what if the direction of a vector quantity which is not due north or due east but somewhere in between north and east? For such cases as this, it is important that there be some convention for describing the direction of such a vector.

One convention upon which we can all agree is sometimes referred to as the CCW convention - counterclockwise convention. Using this convention, we can describe the direction of any vector in terms of its counterclockwise angle of rotation from due east. The direction north would be at 90 degrees since a vector pointing east would have to be rotated 90 degrees in the counterclockwise direction in order to point north. The direction of west would be at 180 degrees since a vector pointing west would have to be rotated 180 degrees in the counterclockwise direction in order to point west. Further illustrations of the use of this convention are depicted by the animation below.

Use the CCW convention when you describe the direction of the displacement in this activity. Determine the angle that the displacement vector (shown in red) makes with east in the counter-clockwise direction.