a farmer moves along the boundary of a square field of side 10 metre in 40 seconds what will be the magnitude of displacement of the farmer at the end of 2minutes 20seconds from his initial position?
Answers
A farmer moves along the boundary of a square field of side 10 m in 40 sec.
Side of square = 10 m and time = 40 sec
Perimeter of square = 4 × side
= 4 × 10 = 40 m
We have to find the displacement of the farmer at the end of 2 min 20 sec.
Time = 2 min 20 sec
1 min = 60 sec
2 min = 2(60) = 120 sec
= 120 sec + 20 sec = 140 sec
Now,
In 1 sec distance covered by farmer = 40/40 = 1 m
So, in 140 sec distance covered by farmer = 1 × 140 = 140 m
Number of rotations to cover 140 m along the boundary = Distance/Perimeter
= 140/40 = 3.5 rounds
Therefore, the farmer takes 3.5 revolutions.
Let us assume that farmer is at the point A from the origin of the square field.
Now,
Displacement = diagonal of square
And from above we have a side of square = 10 m
So, displacement = 10√2 m
Answer:
10√(2) metres.
Step-by-step explanation:
Case 1 :
Time taken for one round = 40 sec.
Distance covered in 40 sec = Perimeter of square = 4*10m = 40 m.
Therefore, Number of rounds covered in 40 sec = 1.
Case 2 :
Time taken = 2 min 20 sec = (2*60+20 ) sec = 120+20 = 140 sec.
Rounds covered in 140 sec = 140/40 = 3.5 rounds or 3 and a half rounds.
So,
After 3 complete rounds, a half round means, the farmer covered 2 sides of the square field ( since square has 4 sides in total and half means 2 sides). So, now, the farmer is diagonally opposite from where he started.
This diagonal distance is the displacement.
This can be calculated by pythagorus theorem after dividing the square into 2 triangles.
According to pythagorus theorem,
(side)^2 + (side)^2 = (diagonal)^2.
So,
10^2 + 10^2 = (diagonal)^2.
100 + 100 = (diagonal)^2.
200 = (diagonal)^2.
Therefore,
Diagonal = √(200)
= √(2) * √(100)
= √(2) * 10
= 10√(2) metres.
So, displacement is equal to 10√(2) metres.
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