A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?
Explanation
Movement
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Initial Position: Let the starting point be O(0,0).
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First Move: He walks 5 km South.
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Second Move: He turns Right. (When facing South, a right turn leads toward the West). He walks 3 km.
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Third Move: He turns Left. (When facing West, a left turn leads toward the South). He walks 5 km.
Mathematical Representation
We can represent the final position (x,y) relative to the starting point (0,0) as follows:
Let Dtotal be the final displacement vector:
x=0(initial)+0(south)−3(west)=−3
y=0(initial)−5(south)−5(south)=−10
The final coordinates are:
Since the x-coordinate is negative (West) and the y-coordinate is negative (South), the direction from the starting point is:
Answer: The man is in the South-West direction from his starting place.
