Question

A farmer moves along the boundary of a square field of side 10m in 40sec. What will be the magnitude of the displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

Answer 1

Hint: In this kind of question, you need to use little geometry and basic math. Use the formula of Pythagoras theorem. In this case, displacement will be equal to the diagonal of a square and use the perimeter formula to calculate the perimeter of a square. Using this formula you will get a number of revolutions completed by a farmer. Convert minutes into seconds.

Complete step by step solution:
In this question, it is given that a farmer walk in a square field having sides equal to 10m. He takes 40 seconds to travel the whole square field. Now we need to find out displacement in 2 minutes and 20 seconds from his initial position.
It is given that the side (s) of the square field is 10 m.
Therefore the perimeter of the square is given by the sum of the sides of the square.
So, perimeter (P) = 10+10+10+10=40m.
We know that time taken to travel 40 m is 40 sec.
Then in one meter, he should have covered 1 meter.
Convert 2minutes 20 seconds into seconds.
So time in seconds is 140second.
Now the distance covered by the farmer in 140 second=140×1=140m.
Calculate a total number of revolutions farmers need to take to cover a distance of 140 meters.
So, $\dfrac{\text{total distance}}{perimeter}=3.5$
Now to calculate displacement, we will take a diagonal in a square field.
We know that the square of hypotenuse is equal to the sum of squares of two sides of a triangle using Pythagora's theorem.
So, $\text{displacement=}\sqrt{{{10}^{2}}+{{10}^{2}}}=14.14m$.
Hence, the magnitude of the displacement of the farmer at the end of 2 minutes 20 seconds from his initial position is 14.14m.

Note: Displacement is the shortest distance between initial and final point. While the distance is the total path covered from initial to final point. In the example given above, it is shown that the person has completed three and a half rounds. As the field was square and the farmer has completed half of the round, the last half round indicates the two sides of square i.e. 20m because square has four sides. So in this case diagonal will be the displacement as it is the shortest distance.