Question

A person walks in the following pattern: 2.9 km north, then 2.8 km west, and finally 4.4 km south. (a) How far and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point

Answer 1

Answer:

(a) Magnitude =3.18 km

(a) Angle =28.2°

Explanation:

(a) To find magnitude of this vector recognize

$R_{x}=-2.8 km\\R_{y}=-1.5km$

Use Pythagorean theorem

$R=\sqrt{(R_{x})^{2}+(R_{y})^{2} }\\ R=\sqrt{(-2.8)^{2}+(-1.5)^{2} }\\ R=3.18km$

(b)To find the angle use the trigonometric property

$tan\alpha =\frac{opp}{adj}\\\ tan\alpha =\frac{R_{y} }{R_{x}}\\\alpha =tan^{-1}(\frac{(-1.5)}{(-2.8)})\\\alpha =28.2^{o}$