a farmer moves along the boundary of a square field of side 10 m in 40 s. what will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?
A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?
Answer:
To find the magnitude of the displacement of the farmer, we need to calculate the total distance covered by the farmer along the boundary of the square field first.
Given that the side of the square field is 10 m, the total distance along the boundary of the square can be calculated as follows:
Perimeter of a square = 4 x side length
Perimeter = 4 x 10 = 40 m
Since the farmer completes one round along the boundary in 40 seconds, the farmer covers a distance equal to the perimeter of the square field in one round.
Now, the time given is 2 minutes 20 seconds, which is equal to 140 seconds (2 minutes x 60 seconds + 20 seconds).
Since the farmer completes one round in 40 seconds, we need to calculate how many complete rounds the farmer makes in 140 seconds:
Number of rounds = Total time / Time for one round
Number of rounds = 140 s / 40 s = 3.5 rounds
Since the farmer cannot complete half a round, the farmer completes 3 full rounds in 140 seconds. Therefore, the total distance covered by the farmer in 140 seconds is 3 rounds x 40 m = 120 m.
The displacement of the farmer at the end of 140 seconds is the distance between the initial and final positions after completing the given number of rounds. Since the farmer moves along the boundary of the square field, the displacement would be the diagonal of the square.
The diagonal of a square can be calculated using the formula:
Diagonal = side length x √2
Diagonal = 10 x √2 ≈ 14.14 m
Therefore, the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position would be approximately 14.14 meters.