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  4. A blind person after walking 10 steps in one direction each of length 80 cm , turns randomly to the left or to right by 90° . After walking a total of 40 steps, the maximum displacement of the person from its starting point can be

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Q. A blind person after walking $10$ steps in one direction each of length $80 \, cm$ , turns randomly to the left or to right by $90^\circ $ . After walking a total of $40$ steps, the maximum displacement of the person from its starting point can be

NTA AbhyasNTA Abhyas 2020Motion in a Straight Line

Solution:

This person cannot walk straight more than 10 steps.
Distance covered in 10 steps
$=10\times 0.8=8$ m
As the person has to turn after every 10 steps, the only way to have maximum displacement is walk as shown in the figure.

Solution
The maximum displacement $=AE=AC+CE$
$=8\sqrt{2}+8\sqrt{2}=16\sqrt{2}m$