Question

A blind person after walking 10 steps in one direction, each of length 80 cm, turns randomly to the left or to the right by 90${}^0$ each time moving 10 steps. After walking a total of 40 steps the maximum displacement of the person from his starting position could be :

• A. 320 m
• B. 32 m
• C. $16\sqrt{2}m$
• D. none

Answer 1

Answer: (C)

$16\sqrt{2}m$

Maximum can be when he moves $20$ in one direction and $2$0 in other perpendicular to it.

Hence, he covered $20\times 0.8=16m$ in $x$ and $y$ direction.
=> Total displacement $=16\sqrt{2}$