Question

Aswin walk 20m north , 12m east , 7m West and 8m south and then stop to drink water what is the magnitude of his displacement from his original point?

Answer 1

${\underline {\boxed {\large {\rm { Displacement = 13 \; m} }}}}$

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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) :–

• AB [ When he moves 20m towards north.]

• BC [ When he moves 12m towards east.]

• CD [ When he moves 7m towards west. ]

• DE [ When he moves 8m towards south.]

Also,

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

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

Now, clearly we can see that :

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

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

In the triangle AOE :

→ AO = AB – OB

→ AO = (20 – 8) m

→ AO = 12 m⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[Perpendicular]

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→ OE = BD [ Opposite sides of a rectangle are equal]

→ OE = 5 m⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[Base]

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→ AE = ? ⠀⠀[Hypotenuse or Displacement]

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By applying pythagoras property :

$\hookrightarrow \sf {H^2 = B^2 + P^2 }$

$\hookrightarrow \sf {(AE)^2 = (OE)^2 + (AO)^2 }$

$\hookrightarrow \sf {(AE)^2 = (5)^2 + (12)^2 }$

$\hookrightarrow \sf {(AE)^2 = 25 + 144 }$

$\hookrightarrow \sf {(AE)^2 = 169 }$

$\hookrightarrow \sf {AE = \sqrt{169} }$

$\hookrightarrow \boxed{\sf {AE = 13 \: m}}$

Therefore, displacement is 13 m.