Question

a blind person after walking 10 steps in one direction each of lenght 80cm turns randomly to the left or to the right by 90°. after walikng a total 40 steps the maximum possible displacement of person from his starting position could be
1. 320m.
2.32m
3.16/√2m
4.16√2m

Answer 1

He took 10 steps of 80cm that is = 10×80 cm
=800cm = 8m
after turning right or left he took 40 steps. that is= 40×80cm=3200cm=32m
His displacement=✓8²+32²=✓64+1024=✓1088
=32.9848...m, or 32m approx.
therefore, correct option is option 2. that is 32m.

Answer 2

The maximum possible displacement of the person is 32m (Option 2)

Given:

1 step = 80cm

To find:

The total displacement

Solution:

• The person first walks 10 steps in one direction.
• Let that path be AB
• Then the distance AB = 10 steps x 80cm = 800cm = 8m
• At point B, the person takes a 90° turn.
• From B he walks 40 steps.
• Let that path be BC.
• Then the distance BC = 40 steps x 80cm = 3200cm = 32m
• AB and BC are perpendicular.
• ABC thus forms a right-angled triangle.
• Displacement is the shortest path traveled.
• The shortest path is AC.
• Therefore, displacement is AC.

AC² = AB² + BC² (Pythagoras Theorem)

       = 8² + 32² = 1088

AC  = √1088 = 32.98

Therefore, the maximum possible displacement is 32m approximately.