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Difficulty: EasyDirection and Distance Test

A delivery courier starts from a central warehouse and travels 5 km5\text{ km} due North. The courier then turns right and travels 12 km12\text{ km} due East, and finally turns right again and travels 5 km5\text{ km} due South. What is the shortest distance and direction of the courier relative to the starting warehouse?

  1. 12 km12\text{ km} to the EastAnswer
  2. B
    12 km12\text{ km} to the West
  3. C
    22 km22\text{ km} to the East
  4. D
    5 km5\text{ km} to the South

Answer

12 km12\text{ km} to the East
Taking the starting warehouse as the origin (0,0)(0,0), moving 5 km5\text{ km} North reaches point (0,5)(0, 5). Turning right (facing East) and walking 12 km12\text{ km} reaches point (12,5)(12, 5). Turning right again (facing South while at (12,5)(12,5)) and traveling 5 km5\text{ km} brings the courier to (12,0)(12, 0). The straight-line distance from (0,0)(0,0) to (12,0)(12,0) is 12 km12\text{ km} in the positive x-direction, which corresponds to 12 km12\text{ km} to the East.

Step-by-Step Solution

1
Analyze vertical (North-South) displacement
The courier moves 5 km5\text{ km} North and later 5 km5\text{ km} South. Net vertical displacement = 5 km−5 km=0 km5\text{ km} - 5\text{ km} = 0\text{ km}.
Equal distances traveled in opposite directions along the vertical axis cancel out completely.
2
Analyze horizontal (East-West) displacement
The courier moves 12 km12\text{ km} East. Net horizontal displacement = 12 km12\text{ km} East.
There are no opposing Westward turns to reduce the Eastward travel.
3
Determine final straight-line position
The courier is located 12 km12\text{ km} due East of the starting warehouse.
Combining zero vertical shift and 12 km12\text{ km} Eastward shift gives a final vector of 12 km12\text{ km} East.

Key Concept

Vector Cancellation and Net Displacement
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Topics

Direction and Distance Test

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