Question

A person moves 30m towards north and 20m towards east and finally 10m to-
wards south. The magnitude of displacement of the person from the origin is
options are
$1) \: 40m$
$2)20 \sqrt{3}$
$3)20 \sqrt{2}$
$4)20( \sqrt{3} - 1)$





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Answer 1

Answer:

40m

hope this helps...

Answer 2

Required Answer :

${\underline {\boxed {\Large {\rm { Option \: C \: (20\sqrt{2} \: m) } }}}}$

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Here, as per the provided question let us draw a rough diagram first. [Refer to the attachment.]

From the given figure (According to the question) :–

• AD [ When a person moves 30m towards north.]
• DC [ When he moves 20m towards east.]
• CB [ When he moves 10m towards south. ]

Also,

• AB [ Displacement ] : As it is the shortest path between his inital and final position.

›» As we can't find the measure of AB directly, so let us break into different shapes to find the displacement (measure of AB).

Now, clearly we can see that :

• ABCD is a quadrilateral having two shapes : A rectangle and a triangle.

›» OB is an imaginary line that is separating both shapes.

In the triangle ABO :

→ AO = AD – OD

→ AO = (30 – 10) m

→ AO = 20 m⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[Perpendicular]

_________________

→ OB = DC [ Opposite sides of a rectangle are equal]

→ OB = 20 m⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[Base]

_________________

→ AB = ? ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\rm \red {{Hypotenuse}_{[Displacement]}}$

_________________

By applying pythagoras property :

→ ${\underline {\underline {\large {\sf { {H}^{2} = {B}^{2}+{P}^{2} } }}}}$

$\sf {\longmapsto {AB}^{2} = {OB}^{2}+{AO}^{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\longmapsto {AB}^{2} = {20}^{2}+{20}^{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\longmapsto {AB}^{2} = 400 + 400}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\longmapsto {AB}^{2} = 800}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\longmapsto AB= \sqrt{800}}$

Now, by prime factorization :

2 | 800

2 | 400

2 | 200

2 | 100

2 | 50

5 | 25

5 | 5

⠀| 1

→ √800 = √2 × 2 × 2 × 2 × 2 × 5 × 5

→ √800 = 2 × 2 × 5 × √2

→ √800 = 4 × 5 × √2

→ √800 = 20 × √2

→ √800 = 20√2

Hence,

$\sf \red {\longmapsto AB= 20\sqrt{2} \: m}$

Therefore, magnitude of displacement of the person from the origin is 20√2 m.