Question

A person walks 5 meters to the east, then turns and walks 7 meters south.

What is their total displacement?

Answer 1

8.6 meters to south east

Step-by-step explanation:

Displacement is change in position or a distance between initial position to final position.

Since a person walks to east and then to the south, it forms a right triangle path. We can use Pythagoras Theorem to help finding the displacement:

`\displaystyle{\vec s = √(s_x^2 + s_y^2)}`

Where
`\displaystyle{\vec s}` is displacement,
`\displaystyle{s_x}` is horizontal distance (east) and
`\displaystyle{s_y}` is vertical distance (south). Therefore:

`\displaystyle{\vec s = √(5^2 + 7^2)}\\\\\displaystyle{\vec s = √(25+49)}\\\\\displaystyle{\vec s = √(74)}\\\\\displaystyle{\vec s = 8.6 \ \, \sf{meters \ \, to \ \, south \ \, east}}`

Therefore, the displacement is 8.6 meters to south east.

(The attachment is added for visual reference on displacement and direction.)