question_answer

A person moves 30 m north and then 20 m towards east and finally \[30\sqrt{2}\] m south-west direction. The displacement of the person from the origin

A) 10 m along north

B) 10 m along south

C) 10 m along west 

D) Zero

Correct Answer: C

Solution :

From figure,     \[\overline{OA}=0\overset\frown{i}+30\overset\frown{j},\] \[\overrightarrow{AB}=20\overset\frown{i}+0\overset\frown{j},\] \[\overline{BC}=-30\sqrt{2}\cos 45{}^\circ \overset\frown{i}-30\sqrt{2}\sin 45{}^\circ \overset\frown{j}\] \[=-30\overset\frown{i}-30\overset\frown{j}\] \[\therefore \text{Net desplacement,}\] \[\begin{align}   & \text{OC=OA+AB+BC=}-10\overset\frown{i}+0\overset\frown{j} \\  & \text{ }\!\!|\!\!\text{ OC }\!\!|\!\!\text{ =10m} \\ \end{align}\]