Question

a farmer moves along the boundary of a square field of side 10 m in 40seconds. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds
​

Answer 1

Answer:

Farmer takes 40 s to move along the boundary. Thus, after 3.5 round farmer will at point C of the field. Thus, after 2 min 20 seconds the displacement of farmer will be equal to 14.14 m north east from initial position.

Answer 2

It is given to us that the farmer moves along the boundary of a square field of side 10 m in 40seconds .

• so , Length of 1 side = 10 m
• Perimeter of square field = 10 × 4 = 40m

and it is asked to find magnitude of displacement of the farmer at the end of 2 minutes 20 seconds

• 2min 20sec = 140 sec

Now we know that the farmer moves 40 m in 40 sec

$\begin{gathered}\begin{gathered}\begin{gathered}\sf \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c|c |c|} & \bf\bf No. of rounds (distance)(time) & \bf Displacement\\ \\ & \rm\rm 1 \: (40m)(40sec) & 0 \\ \\ & \rm\rm 1 \: (40m)(40sec) & 0 \\ \\ & \rm\rm 1 \: (40m)(40sec) & 0 \\ \\ & \rm\rm \dfrac{1}{2}(20m)(20sec) & \rm ? \\ \\ \rm total & \rm 3\dfrac{1}{2} \: (140m)(140sec)& \rm ? \end{array}}}\end{gathered}\end{gathered} \end{gathered} \end{gathered}\end{gathered}\end{gathered} \end{gathered}$

Now see the figure , ABCD (see in the attachment )

• A is the initial point
• B is the final point

We know that Displacement is measured as a shortest distance between the initial and final position of the moving body

Hence , we need to Find the length of A and C

So , by using Pythagoras theorem we get ,

$\begin{gathered} \longmapsto \rm {{AC} ^{2} =AB ^{2} + BC ^{2} }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm {{AC} ^{2} = 10 ^{2} + 10 ^{2} }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm {{AC} ^{2} = 100 + 100 }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm {{AC} = \sqrt{100 + 100} }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm {{AC} = \sqrt{200} }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm {{AC} = 10\sqrt{2} }\\ \end{gathered}$

$\begin{gathered} \longmapsto \rm\bold {{AC} = 14.14m }\\ \end{gathered}$