A person walks in the following pattern: 3.4 km north, then 2.2 km west, and finally 4.9 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 with Explanation:

We are given that

Person walks in north direction=3.4 km

Person walks in west direction=2.2 km

Person walks in south direction=4.9 km

a.We have to find the distance flawn by bird in a straight line from the same starting point to the same final point.

x-Component of resultant vector=-2.2 km

y-Component of resultant vector=

Magnitude of resultant vector =

By using the formula of magnitude of vector

r=xi+yj

Substitute the values

b.We have to find the direction .

By using the formula

S of W

Resultant vector lies in III quadrant therefore, in III quadrant the angle

Nof E

Hence, the angle measured from the east in counterclockwise direction=214.2 degree

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day