Question

Ali walks 680m south 780m east 80m south find the distance and the displacement?

Answer 1

$S=S_1+S_2+S_3$,

where, $S$ - overall traveled distance, $S_1 = 680 \; m$ - the first path segment to the south, $S_2 = 780 \; m$ - path segment to the east, $S_3 = 80 \; m$ - the second path segment to the south.

$S=680+780+80=1540 \; m = 1.54 \; km$

$D=\sqrt{D_s^2 + D_e^2}$,

where $D$ - overall displacement, $D_s=S_1 +S_3= 680+80=760 \; m$ - overall displacement to the south, $D_e=S_2=780 \; m$ - displacement to the east.

$D=\sqrt{760^2 + 780^2}=\sqrt{577600 + 608400}=\sqrt{118000} \approx 1089 \; m \approx 1.09 \; km$