Question

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

• A. zero
• B. $28m$ towards south
• C. $10m$ towards south
• D. $15m$ towards south

Answer 1

Answer: (A)

Resolving displacement $30\sqrt{2}m$ south-west into two rectangular components, we get
Displacement in south
$=30\sqrt{2}cos45^{°}$
$=30\sqrt{2}\times \left(\frac{1}{\sqrt{2}}\right)$
$=30m$
Displacement in west
$=30\sqrt{2}sin45^{°}$
$=30\sqrt{2}\times \left(\frac{1}{\sqrt{2}}\right)$
$=30m$
$\therefore$ Effective displacement due to $30m$ north and $30m$ south is zero.
Also effective displacement due to $30m$ east and $30m$ west is zero.