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 south - negative and north - positive

Let south - ward displacement be negative and north - ward displacement be positive. The first displacement $d_1=- 6.2$ km, the second displacement $d_2 = 9.3$ km, and the third displacement $d_3=-4.3$ km.

Step2: Calculate the net displacement

The net displacement $D=d_1 + d_2 + d_3$. Substitute the values: $D=-6.2+9.3 - 4.3$. First, $-6.2+9.3 = 3.1$ km, then $3.1-4.3=-1.2$ km.

Answer:

1.2 km South