Question

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

• A. Zero
• B. 28 m towards south
• C. 10 m towards west
• D. 15 m towards east

Answer 1

Answer: (A)

Zero

Answer 2

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

Displacement in south

$= 30 \sqrt { 2 } \cos 45 ^ { \circ } = 30 \sqrt { 2 } \times \left( \frac { 1 } { \sqrt { 2 } } \right) = 30 \mathrm {~m}$

Displacement in west

$= 30 \sqrt { 2 } \sin 45 ^ { \circ } = 30 \sqrt { 2 } \times \left( \frac { 1 } { \sqrt { 2 } } \right) = 30 \mathrm {~m}$

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

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