Question

a farmer moves along a boundary

Answer 1

In 40 sec, he covers the square. In 10 seconds he covers one side.
We want displacement after 140 seconds.
Let the sides of the square be A,B,C,D in the order of his walking. The in 120 seconds, he make 3 full rounds.  In the remaining 20 seconds, he covers side A and side B.
He is at the opposite end of the diagonal at 140 sec.
Displacement is 10√2  = 14.14 meters from initial position

Answer 2

Answer:The answer, the displacement is 10√2 m

Explanation:

Look, let's note all the given info,

Side of the field = 10m

Time taken to walk along the boundary of the square field = 40s

Time given to calculate the displacement = 2 min 20 s= 2×60 + 20

=140s

Total distance walked by him in 140s =

40s=> 40m

140s => 'x'

Therefore, x = 140×40/40= 140 m

That means, distance covered by him in time 2 min 20s = 140m

Perimeter of the field = 10×4 = 40 m

No. Of rounds taken = 140/40 = 4.5

That means, he didn't complete the 4th time.

Now imagine, make a right angled triangle, from the point the farmer started to the point where he ended ine the second side. Look at the diagram, attached here.

So, it's a right angled triangle,

By Pythagoras theorem,

(Side) ^2 = √(10) ^2 +(10) ^2

Side2 = √100 + 100=√200

Side = 10√2m ..... ( taking square root of both sides)

{ here side means side of a right angled triangle}

Displacement = final - initial position

= 10√2-0= 10√2m

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