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Question

A farmer moves along the boundary(starting from A) of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds ?

245347_9da37d952b9c4f1da3e8f61f37fdd205.png

A
14.14 m
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B
5 m
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C
15.06 m
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D
14.19 m
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Solution

The correct option is B 14.14 m
The perimeter of square field
ABCD=4×10m=40m.
Time for moving around the 10m square field once =40s.
Time for journey of farmer =2min and 20s=140s.
Number of times the farmer moved around the square field =14040=312times.
For going once around the 'square field, the displacement =0
For going thrice around the square field, the displacement =0
For going 12 around the square field, the distance covered =40×12=20m.
It is obvious from the figure, that if the farmer starts from point A, then he will cover 10m along AB and then 10m along BC.
Therefore, displacement of farmer from the point A to point C is
AC=AB2+BC2
=102+102
14.14 m

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