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

Solution

Given,

Side of the given square field = 10m

Hence, the perimeter of a square = 40 m

Time taken by the farmer to cover the boundary of 40 m = 40 s

So, in 1 s, the farmer covers a distance of 1 m

Now, 

Distance covered by the farmer in 2 min 20 sec = 1 x 140 = 140 m

So,

The total number of rotations taken by the farmer to cover a distance of 140 m = total distance/perimeter

= 3.5

At this point, let us say the farmer is at point B from the origin O

Therefore, from Pythagoras theorem, the displacement s = √(10²+10²)

s = 10√2

s = 14.14 m