Answer:
First, let's write some definitions.
Displacement is the distance between the final position and the initial position.
Here we can define north as the positive direction and south as the negative one.
First, we assume that the initial position is 0m
We know that she first goes 43m north
Then she goes 38m south
Then she goes 16m north
And then she goes south again for X meters, such that the total distance traveled is 122m
The total distance traveled is the sum of all distances traveled, regardless of the direction
then we have:
43m + 38m + 16m + X = 122m
Solving this for X we get:
97m + X = 122m
X = 122m - 97m = 25m
So she finally goes 25m south.
Now let's analyze how her position changes:
First, she starts at 0m
Then she goes north for 43m, then her new position is:
0m + 43m = 43m
Now she goes 38m south, then her new position is:
43m - 38m = 5m
Then she goes north again, for 16m
Then the new position is:
5m + 16m = 21m
Now she goes south for 25m, then the final position is:
21m - 25m = -4m
The displacement is equal to the difference between the final position and the initial one, so the displacement is:
-4m - 0m = -4m
The displacement is -4m.
