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

(a) Magnitude =3.18 km

(a) Angle =28.2°

Step-by-step 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 =(opp)/(adj)\\\ tan\alpha =(R_(y) )/(R_(x))\\\alpha =tan^(-1)(((-1.5))/((-2.8)))\\\alpha =28.2^(o)`