Question

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

Answer 1

Given:

Length of side of square field, a= 10m

Time taken by farmer to complete 1 round of field, t= 40 s

To Find:

Magnitude of the displacement at the end of 2 min 20 s

Solution:

We know that,

• Length of diagonal d of square is given by

$\pink{\boxed{\bf{d=\sqrt{2}\ a}}}$

where a is the length of side of square

• Displacement is the shortest distance between starting and final position.

$\rule{190}{1}$

Given time t is

$\longrightarrow\rm{t=2\:min\:+20\:s}$

$\longrightarrow\rm{t=2\times60\:s\:+20\:s}$

$\longrightarrow\rm{t=120\:s\:+20\:s}$

$\longrightarrow\rm{t=140\:s}$

$\rule{190}{1}$

Now,

Rounds completed by farmer in 40s= 1

Rounds completed by farmer in 1s= $\rm{\dfrac{1}{40}}$

Rounds completed by farmer in 140s=$\rm{\dfrac{1}{40}\times140}$

or

Rounds completed by farmer in 140s= $\rm{3.5}$

That means farmer covers 3 and a half round in 140s

$\rule{190}{1}$

Let the diagonal of given square be d

So,

$\longrightarrow\rm{d=\sqrt{2}\ a}$

$\longrightarrow\rm{d=\sqrt{2}\times10 }$

$\longrightarrow\rm{d=10\sqrt{2}\ m}$

$\rule{190}{1}$

Let the displacement of farmer be 'D'

Considering that farmer has started taking round from one of the corner of square field

Since, after covering 3 and half rounds of field final position of farmer is opposite corner to starting position

So,

$\longrightarrow\rm{D=d}$

$\longrightarrow\rm\green{D=10\sqrt{2}\:m}$

Hence, the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds is 10√2 m.

Answer 2

Given:-

• Distance covered by farmer 10m in 40s.

• Time = 2 min 20s = 60×2 +20=140s

To Find:-

• Displacement of farmer at the end of 2 min 20 second.

Solution :-

According to the Question

Total distance covered by farmer 10m in 40s

Total Time taken by farmer =140s

If he covered 1 round of square field in 40s.

No. of round = Total distance /total time =140/40=3.5 round

∴ He covered 3.5 round in 140s

We know that the displacement is the shortest path between two points.

AC is the displacement

By using Pythagoras theorem

➦AC² = AB² + BC²

➭ AC² = 10²+ 10²

➭ AC² = 100+100

➭ AC² =200m

➭ AC = √200m

➭ AC = 10√2

➭ AC = 14.142m

∴ The displacement of farmer after 140s is

14.142 m