A person walks in the following pattern: 3.1 km north, then 2.4 km west, and finally 5.2 km south. (a) Sketch the vector diagr

Question

A person walks in the following pattern: 3.1 km north, then 2.4
km west, and finally 5.2 km south.
 (a) Sketch the vector diagram
that represents this motion.
 (b) How far and (c) in what direction
would a bird fly in a straight line from the same starting point to
the same final point?

BoomSchroasted · Answer

Well, separate all the different directions into components.  North/South will be the Y component, and East/West will be the X component. (North = +... South = -) (East = +... West = -)
 
Y = +3.1, -5.2
X = -2.4
 
Simplify these using addition/subtraction.
 
Y = -2.1
X= -2.4
 
On a graph, go -2.4 units down along the X axis and make a point.
Go -2.1 units down along the Y axis and make a point.  Where these points come and meet in the middle is the finishing vector graph.  Now, from this point, draw a straight line back to the point of origin (0,0), and there is your vector.
 
Using this as a triangle, and the pythagorean theorem, the bird travels 3.19 km if he goes along the straight vector.
 
The angle is -48.829 degrees.

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A person walks in the following pattern: 3.1 km north, then 2.4 km west, and finally 5.2 km south. (a) Sketch the vector diagr

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