Answer:
The displacement is about 4.47 miles
Explanation:
Displacement
Is the vector that represents the difference in positions that an object has moved on.
If the object was at position [tex]\vec p_1[/tex] and ended up in the position [tex]\vec p_2[/tex], then the displacement is:
[tex]\vec d=\vec p_2- \vec p_1[/tex]
The magnitude of d is the length of the vector. Given its rectangular coordinates (dx,dy), then the magnitude is:
[tex]\mid d\mid=\sqrt{dx^2+dy^2}[/tex]
If you walk 2 miles east from the origin, your new position is (2,0). When you now walk 4 miles north, your final position is (2,4).
The displacement is:
[tex]\vec d=(2,4)-(0,0)=(2,4)[/tex]
And its magnitude is:
[tex]\mid d\mid=\sqrt{2^2+4^2}[/tex]
[tex]\mid d\mid=\sqrt{4+16}[/tex]
[tex]\mid d\mid=\sqrt{20}[/tex]
[tex]\mid d\mid\approx 4.47\ miles[/tex]
The displacement is about 4.47 miles
