A baseball player runs 27.4 meters from the batter’s box to first base, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player’s total displacement from the batter’s box is
30.0 meters.
The total distance traveled by the player is the sum of the distance from the batter's box to first base, the distance the player overran first base, and the distance back to first base.
Total distance = 27.4 m + 3.0 m + 3.0 m = 33.4 meters
The total displacement of the player is the straight-line distance from the batter's box to the final position at first base. This is a distance of 30.0 meters (27.4 m + 3.0 m).
Therefore, the magnitude of the player's total displacement from the batter's box is 30.0 meters.