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Q.
A person moves $30\,m$ north, then $30\,m$ east, then $=30\sqrt{2}\,m$ south-west. His displacement from the original position is
Motion in a Plane
Solution:
Resolving displacement $30\sqrt{2}\,m$ south-west into two rectangular components, we get
Displacement in south
$=30\sqrt{2}\,cos\,45^{°}$
$=30\sqrt{2}\times\left(\frac{1}{\sqrt{2}}\right)$
$=30\,m$
Displacement in west
$=30\sqrt{2}\,sin\,45^{°}$
$=30\sqrt{2}\times \left(\frac{1}{\sqrt{2}}\right)$
$=30\,m$
$\therefore $ 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.