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

Question

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 (A) Zero (B) 8√2m (C) 16√2m (D) 32m

Tardigrade Admin · Accepted Answer

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

= A E = A C + CE

= 82 + 82 = 162 m

Q. A blind person after walking $10$ steps in one direction each of length $80 c m$ , turns randomly to the left or to right by $9 0^{\circ}$ . After walking a total of $40$ steps, the maximum displacement of the person from its starting point can be

Zero

$82 m$

$162 m$

$32 m$

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.

The maximum displacement $= A E = A C + CE$
$= 82 + 82 = 162 m$

Q. A blind person after walking 10 steps in one direction each of length 80cm , 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

Zero

82​m

162​m

32m

This person cannot walk straight more than 10 steps. Distance covered in 10 steps =10×0.8=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. The maximum displacement =AE=AC+CE =82​+82​=162​m

Q. A blind person after walking $10$ steps in one direction each of length $80 c m$ , turns randomly to the left or to right by $9 0^{\circ}$ . After walking a total of $40$ steps, the maximum displacement of the person from its starting point can be

$82 m$

$162 m$

$32 m$

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.

The maximum displacement $= A E = A C + CE$
$= 82 + 82 = 162 m$