a farmer moves along the boundary of a square field of side 10m in 40 seconds. What will be the magnitude of displacement and distance of the farmer at the end of 2 minutes 20 second. (14.14m, 140m)
Answers
Explanation:
The farmer takes 40 seconds to cover 4 × 10 = 40 m.
In 2 min and 20 s (140 s), he will cover a distance = (40/40) × 140 = 140 m.
Therefore, the farmer completes (140/40) = 3.5 rounds (3 complete rounds and a half round) of the field in 2 min and 20 seconds.
Displacement =14.14m
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As per given condition, 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.
Using Pythagorean theorem,
(diagonal)² = (side)² + (side)²
(diagonal)² = (10)² + (10)²
diagonal = √(100 + 100)
diagonal = √200
diagonal = 10√2
Displacement by farmer is 10√2 or 14.14 m.