Zamir and Talia raced through a maze. Zamir walked 2 m north, 2 m east, 4 m south, 2 m east, 4 m north, 2 m east, 3 m south, 4 m east and 4 m north. Talia walked 2 m north, 6 m east, 3 m south, 4 m east, and 4 m north.
Compare their displacements:
Zamir’s displacement is
Talia’s displacement.
Zamir's displacement is the vector sum of all his individual movements. We can break it down into components:
North: 2 m - 4 m + 4 m - 3 m = -1 m
East: 2 m + 2 m + 2 m + 4 m = 10 m
Therefore, Zamir's displacement is sqrt((-1)^2 + 10^2) = sqrt(1 + 100) = sqrt(101) = 10.05 m
Talia's displacement is:
North: 2 m - 3 m = -1 m
East: 6 m + 4 m = 10 m
Therefore, Talia's displacement is sqrt((-1)^2 + 10^2) = sqrt(1 + 100) = sqrt(101) = 10.05 m
Therefore, Zamir's displacement is equal to Talia's displacement.