Question

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

Answer 1

Answer:

After 3.5 round farmer will at point C of the field.

Explanation:

Here,

Side of the given square field = 10m

So,

perimeter of a square = 4*side = 10 m × 4 = 40 m

Farmer takes 40 s to move along the boundary.

Displacement after 2 minutes 20 s = 2 × 60 s + 20 s = 140 seconds

Since in 40 s farmer moves 40 m

• In 1s the distance covered by farmer = 40 / 40 m = 1m

• In 140s distance covered by farmer = 1 × 140 m = 140 m.

Now,

Number of rotation to cover 140 along the boundary = $\frac{total(distance)}{perimeter}$

= 140 m / 40 m = 3.5 round

Thus,

After 3.5 round farmer will at point C of the field.

Answer 2

$\large\bf\underline {To \: find:-}$

• Displacement of farmer at the end of 2 minutes and 20 seconds

$\huge\bf\underline{Solution:-}$

$\star\bf\underline{Given:-}$

• Side of square field = 10m
• farmer moves along the boundary of a square field of side 10m in 40s.

we know that,

☘️ perimeter of square = 4 × side

⪼ perimeter of square = 4 × 10

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀= 40m

Time taken by farmer to cover 40m = 40s

So,

In 1 second the farmer covers 1meter distance.

Now,

Distance covered by the farmer at the end of 2 minutes and 20 seconds:-

Time = 2minute 20 second

Converting 2 minutes into seconds:-

= 2 × 60 + 20

= 120 + 20

= 140 second

As we know that, the farmer covers 1m distance in 1 sec ,

So,

Distance covered by the farmer at the end of 2 minutes and 20 seconds is :-

= 1 × 140

= 140m

So,

The farmer will cover 140m distance in 2 minutes and 20 seconds.

Now,

Number of rotation the farmer takes to cover the distance

= Total Distance/perimeter

= 140/40

= 3.5

If the farmer stars from A( initial position) then after 3.5 rounds he was at point C.

Therefore, Displacement is AC.

● By using Pythagoras theorem,

• AC² = AB² + BC²

➛ AC² = 10² + 10²

➛ AC² = 100 + 100

➛ AC² = 200

➛ AC = √200

➛ AC = 10√2

• ● AC = 14.14m

Hence Displacement of farmer at the end of 2 minutes and 20 seconds is 14.14m

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