Question

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?

• A. $19.05m$
• B. $1.4m$
• C. $14.14m$
• D. $24.14m$

Answer 1

The correct option is C $14.14m$


Given, side of the square field = 10 m
Therefore, perimeter = $10m\times 4=40m$
The farmer moves along the boundary in 40 s.
Displacement after $2m20s(=2\times 60s+20s=140s)=?$
Since in 40 s the farmer moves 40 m, in 1s distance covered by farmer = $\frac{40m}{40}=1m$
Therefore, in 140s distance covered = $140m$.
Number of rounds covered $=\frac{140m}{40m}=3.5$ rounds
If the farmer starts from point A, after 3.5 rounds he will at point C of the field.
Therefore, displacement $AC=\sqrt{(10m{)}^2+(10m{)}^2}$
$=\sqrt{100m^2+100m^2}$
$=\sqrt{200m^2}$
$=10\sqrt{2}m$
$=10\times 1.414m=14.14m$