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

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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.**