A farmer moves along the boundary of a square field of side 10 met in ...
Problem:
A farmer moves along the boundary of a square field of side 10 meters in 40 seconds. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?
Approach:
To solve the problem, we need to find the distance traveled by the farmer in 2 minutes 20 seconds and the direction of his final displacement. The farmer moves along the boundary of a square field of side 10 meters, which means that he covers a distance of 40 meters in each round. Therefore, the total distance covered by the farmer in 2 minutes 20 seconds is:
Calculations:
Total time = 2 minutes 20 seconds = 140 seconds
Total distance covered = (40 meters/round) x (140 seconds/40 seconds/round) = 140 meters
Now, to find the magnitude of displacement, we need to find the straight-line distance between the starting point and the ending point of the farmer. As the farmer moves along the boundary of a square field, he covers the same distance in all four directions. Therefore, the displacement of the farmer is equal to the length of one of the diagonals of the square field. The length of the diagonal can be found using the Pythagorean theorem:
Diagonal of the square field:
Length of one side of the square = 10 meters
Length of diagonal = √(10² + 10²) = √200 ≈ 14.14 meters
Answer:
Therefore, the magnitude of the displacement of the farmer at the end of 2 minutes 20 seconds is approximately 14.14 meters.