Final answer:
The total displacement of the football coach is calculated by the sum of eastward and westward movements, which results in a displacement of 6 meters east, not matching the provided options.
Step-by-step explanation:
The question is asking to calculate the total displacement of a football coach who has moved in a series of directions. Displacement, being a vector quantity, considers both the magnitude and direction of movement. The coach's movements can be summarized and combined as follows:
First, walking 18 m westward, which we can denote as -18 m (since west is typically considered negative).
Then walking 12 m eastward, which is +12 m (east is positive).
Next walking 28 m westward, another -28 m.
Finally, walking 40 m eastward, which is +40 m.
When these movements are combined, the total displacement is calculated by adding these values:
(-18 m) + (+12 m) + (-28 m) + (+40 m) = -18 m +12 m - 28 m + 40 m = 6 m eastward. Therefore, the correct answer is 6 meters east.
The mistake made in the initial question suggesting east and west final displacements (options a, b, c, and d) might have resulted from not considering the correct order and directions of movements; however, based on the information provided, these options are incorrect as the correct displacement is 6 meters east.