A person moves 30 m north, then 30 m east, then m south-west. His displacement from the original position is

Question

A person moves 30 m north, then 30 m east, then $30 \sqrt{2}$ m south-west. His displacement from the original position is

Smart Achievers · Accepted Answer

(1)

Resolving displacement $30 \sqrt{2}$ m south-west into two rectangular components, we get

Displacement in south $= 30 \sqrt{2} \cos 45 ° = 30 \sqrt{2} \times (\frac{1}{\sqrt{2}}) = 30 m$

Displacement in west $= 30 \sqrt{2} \sin 45 ° = 30 \sqrt{2} \times (\frac{1}{\sqrt{2}}) = 30 m$

$∴$ Effective displacement due to 30 m north and 30 m south is zero.

Also effective displacement due to 30 m east and 30 m west is zero.

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