Question

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

Answer 1

Given:

• Side of Square = 10m, thus
• Perimeter P = 40m
• Time taken to cover the boundary of 40 m = 40 s
• Thus in 1 second, the farmer covers a distance of 1 m

⟼ Now distance covered by the farmer in 2 min 20 seconds = 1 × 140 = 140m

⟼ Now the total number of rotation the farmer makes to cover a distance of 140 meters = $\frac{Total \:distance}{Perimeter}$

= 3.5

⟼ At this point, the farmer is at a point say B from the origin O

⟼ Thus the displacement s = $\sqrt{ {10}^{2} + {10}^{2} }$

⟼ From Pythagoras theorem.

S = $10 \sqrt{2}$

•°• S = 14.14m

Answer 2

Explanation:

Farmer takes 40 s to move along the boundary. Thus, after 3.5 round farmer will at point C of the field. Thus, after 2 min 20 seconds the displacement of farmer will be equal to 14.14 m north east from initial position.