The traveler moves 18.6 km east , 27.6 km south east and 9.1 km south.
The distance moved towards the east is 18.6 + 27.6/sqrt 2
The distance moved towards the south is 9.1 + 27.6/sqrt 2
This gives the magnitude of the total displacement as sqrt[(18.6 + 27.6/sqrt 2)^2 + (9.1 + 27.6/sqrt 2)^2]
=> 47.66 km.
The direction of displacement makes an angle equal to arc tan[((18.6 + 27.6/sqrt 2)/(9.1 + 27.6/sqrt 2)]
=> 53.1 degrees in the clockwise direction to the axis pointing east
The displacement of the traveler is 47.66 km in the direction 53.1 degrees clockwise to the axis pointing east
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.