A softball player leaves the batter's box, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, how much smaller or larger is the magnitude of the player's total displacement from the batter's box?

The distance traveled during his run is 6 meters more than his displacement. Displacement only depends on the end points. The route taken is irrelevant to displacement.

Answered by AL2006 | 2024-06-10

The question involves understanding the difference between distance traveled and displacement. When a softball player leaves the batter's box, runs past first base by 3.0 meters, and then returns to first base, the total distance they travel is the sum of the distance to first base, beyond it, and back.
Assuming the distance from the batter's box to first base is also 27 meters (typical for softball/baseball), the player runs 27 meters to first base, 3 meters past it, and then 3 meters back to first base, totaling 33 meters traveled. However, the displacement is the vector from where the player started to where they ended, which is exactly 27 meters, the direct distance from the batter's box to first base.
In this context, the magnitude of the player's total displacement from the batter's box (27 meters) is 6 meters smaller than the total distance traveled (33 meters). This illustrates the key concept that while distance measures the total path length traveled without direction, displacement measures the change in position and direction from the starting point to the endpoint, thus can sometimes be less than the actual distance traveled.

Answered by EveArden | 2024-06-24

The softball player travels a total distance of 7.0 meters while their displacement is 0 meters because they return to the starting point. This means the magnitude of the distance is significantly larger than the displacement. Thus, the player's total distance traveled is larger than their displacement.
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Answered by AL2006 | 2024-10-02