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A farmer walks along the boundary of a square field with side 11 m, completing one round in 20 seconds. After walking for 3 minutes and 20 seconds, what is the magnitude of the displacement from his starting point?
11 m
15.56 m
22 m
0 m
0 m
Determine the total number of rounds by dividing total time by time per round; if the result is an integer, the farmer is back at the starting point, making displacement zero.
Determine the total number of rounds by dividing total time by time per round; if the result is an integer, the farmer is back at the starting point, making displacement zero.
Calculate Total Time
Convert the total walking time into seconds: 3 minutes and 20 seconds = (3 * 60) + 20 = 200 seconds.
Calculate Number of Rounds
The farmer takes 20 seconds to complete one round. Total rounds = 200 seconds / 20 seconds per round = 10 full rounds.
Determine Displacement
Since the farmer completes exactly 10 full rounds, he returns to the exact starting position on the square field. Displacement is defined as the shortest distance between the starting and ending points, which is 0 meters.
A: 11m corresponds to one side of the square, which would only be reached after 5 seconds. B: 15.56m is the length of the diagonal, reached after 10 seconds. C: 22m corresponds to two sides of the square, reached after 10 seconds.
D is correct because the farmer completes exactly 10 full rounds, returning to the starting point where the net displacement is 0 m.
In any perimeter-based movement problem, always check if the total time is a multiple of the time taken for one full round; if it is, the displacement is always zero regardless of the shape's side length.
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