HERE WE GOOOO
To find the coach's overall displacement, we need to calculate the net change in his position from the starting point (the 50-yard line) to his final position (the 30-yard line).
Here are the steps of his movement:
1. He starts at the 50-yard line (A).
2. He walks to the 10-yard line (B), which is a displacement of -40 yards (50 - 10 = -40).
3. He turns around and walks to the 40-yard line (C), which is a displacement of +30 yards (10 - 40 = +30).
4. He turns around again and walks back to the 0-yard line (D), which is a displacement of -40 yards (40 - 0 = -40).
5. Finally, he turns around once more and walks back to the 30-yard line (E), which is a displacement of +30 yards (0 - 30 = +30).
Now, calculate the net displacement by summing these displacements:
-40 yards + 30 yards - 40 yards + 30 yards = -20 yards
The coach's overall displacement is -20 yards. The negative sign indicates that he ended up 20 yards behind his starting point.