Question

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
(1) 3.0 m shorter (3) 3.0 m longer
(2) 6.0 m shorter (4) 6.0 m longer

Answer 1

Answer:

(2) 6.0 m shorte.

Explanation:

Total distance = Distance from batter’s base to first base + Distance covered in overrunning + Distance covered in returning to first base  

Total Distance = 27.4 + 3 + 3 = 33.4 m

Total displacement = Displacement from batter’s base to first base + Displacement covered in overrunning + Displacement covered in to returning first base  

The 2nd and 3rd term will have same magnitude but opposite direction so, they will cancel out each other. Hence,  

Total Displacement = 27.4 m  

Hence, displacement will be 6.0 m shorter than distance.

Answer 2

Distance is a measure of the length of space covered over a certain period of time. While displacement is the change in position of an object from its starting point. Displacement is 6.0 meters shorter than distance.

• Starting position = batter'box

• Batter's box to first base = 27.4 meters

• Distance beyond first base = 3 metres

• Final position = first base

Total distance covered :

(Batter's box - > first base) + (beyond first base) + (return to first base)

• (27.4 + 3 + 3) = 33.4 meters

Total Displacement :

(Batter's box - > first base) + (beyond first base) - (return to first base)

• (27.4 + 3 - 3) = 27.4 meters

Difference in magnitude of Distance and Displacement :

• 33.4 - 27.4 = 6.0 meters

Therefore, displacement is 6m shorter

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