Question

a woman runs 6.2 km south. she then turns around and runs 9.3 km north and then finally turns around once more and runs 4.3 km south. how far and in what direction is she from where she started?
1.2 km south
1.5 km north
3.1 km north
1.2 km north

Explanation:

Step1: Define directions as positive/negative

Let south - ward be negative and north - ward be positive.

Step2: Calculate net displacement

The displacements are $d_1=- 6.2$ km, $d_2 = 9.3$ km, $d_3=-4.3$ km. The net displacement $D=d_1 + d_2 + d_3=-6.2+9.3 - 4.3$.
First, $-6.2+9.3=3.1$ km. Then $3.1-4.3=-1.2$ km.

Answer:

A. 1.2 km South