What is the traveller's total displacement if he moves 18.6 km east , 27.6 km south east and 9.1 km south?

We'll assign coordinate axis to all
directions:

- the positive x axis represents east
direction;

- the negative x axis represents west
direction;

- the positive y axis represents north
direction;

- the negative y axis represents south
direction;

South-east is the direction at 45 degrees to he
positive x axis and the negative y axis and it represents the bisectrix of the 4th
quadrant, where x coordinate is positive and y coordinate is
negative.

We'll calculate the x axis
position:

x = 18.6 + 27.6*cos
45

x = 38.11

We'll calculate
the y axis position:

y = -9.1 - 27.6*sin
45

y = -28.61

Now, we'll
calculate the traveler's total displacement using Pythagorean
teorem:

D = sqrt (x^2 + y^2)

D
= sqrt (1452.3721 + 818.5321)

D = sqrt
2270.9042

D = 47.65
Km

The traveler's total displacement is D =
47.65 Km.