question_answer

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

A)  10 m along north  

B)  10 m along south       

C)  10 m along west         

D)  0.

Correct Answer: C

Solution :

In context to figure, the displacement \[\overrightarrow{OC}\]of the person is given by \[\overrightarrow{OC}=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BC}\] or,\[\overrightarrow{OC}=30\,\hat{J}+20\hat{i}-30\sqrt{2}\cos {{45}^{o}}\hat{i}-30\sqrt{2}\sin {{45}^{o}}\hat{j}\]\[=(30-30)\hat{j}\,+(20-30)\hat{i}\] \[=10\,\hat{i}\] So, the displacement of the person is 10 m along west. Hence, the correction option is [c].