The farmer covers the entire boundary of the square field in 40 seconds
The magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position
The total distance travelled by the farmer in 40 seconds is 4*(10) = 40 meters.
Therefore, the average distance covered by the farmer in one second is: 40m/40 = 1m
Two minutes and 20 seconds can be written as (2 x 60) + 20=140 seconds.
The total distance travelled by the farmer in this timeframe is: 1 m * 140 = 140m
Since the farmer is moving along the boundary of the square field, the total number of laps completed by the farmer will be: 140m/40 = 3.5 laps
Now, the total displacement of the farmer depends on the initial position. If the initial position of the farmer is at one corner of the field, the terminal position would be at the opposite corner (since the field is square).
Hence here, in this case, the total displacement of the farmer will be equal to the length of the diagonal line across the opposite corners of the square.
On applying the Pythagoras theorem,
The length of the diagonal is given as:
√(102+102)= √200= 14.14m.
This is the maximum possible displacement of the farmer.
If the initial position of the farmer is at the mid-point between two adjacent corners of the square, the net displacement of the farmer would be equal to the side of the square, which is 10m. This is the minimum displacement.
When the farmer starts at a random point around the perimeter of the square, his net displacement after travelling 140m will lie between 10m and 14.14m.