A farmer moves along the boundary of a square field of side 10m in 40s. (see down for the question).?

Question

what will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?

Answer 1

displacement = final position - initial position.
Because the path is a square, you need two coordinates (x, y) to specify position. Besides the start poit must be specified.

If we place the rectangle over the 4th quadrant, and the farmer starts walking from the corner at point (0, 0) and moving clockwise then he will move 140 m in 140 s (2 min 20 sec)(because he moves 40 m in 40 s, speed: 1 m/s)

At the end he will move around the square 3 times and a half, it means he is in the opposite corner where he started.
The displacement is the diagonal of the square, that you can calculate by Pithagoras' theorem:
D = sqrt(10² + 10²) = 14.14 m

If he starts moving from another initial position, the displacement could be different.

Answer 2

Assuming he's limited to the boundary of the field, then after 40s he's at one corner, after 2 x 40 seconds or 1min 20 he's at the opposite corner, after 2 min he's at the third corner, and after a further 20 seconds he's halfway down heading towards 4th base (if you like), so the magnitude would be 5 metres.

Answer 3

To complete the square once he requires 4x40= 160 seconds.

He has actually walked for 2m 20 s + 140 seconds.

He has to walk for further 20 seconds or 5m to complete the square.

Answer 4

Ans. 5 meter
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