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                                                 [J & K CET 2004]                       

A)                         10 m along north        

B)                         10 m long south

C)                         10 m along west            

D)                                  Zero

Correct Answer: C

Solution :

                            From figure, \[\overrightarrow{OA}=0\ \overrightarrow{i}+30\ \overrightarrow{j}\], \[\overrightarrow{AB}=20\ \overrightarrow{i}+0\ \overrightarrow{j}\]                                     \[\overrightarrow{BC}=-30\sqrt{2}\ cos{{45}^{o}}\overrightarrow{i}\]\[-30\sqrt{2}\ \sin \text{4}{{\text{5}}^{\text{o}}}\overrightarrow{j}\] \[=-30\ \overrightarrow{i}-30\ \overrightarrow{j}\]             \ Net displacement, \[\overrightarrow{OC}=\overrightarrow{OA}+\overrightarrow{AB}+\overrightarrow{BC}\]        \[=-10\ \overrightarrow{i}+0\ \overrightarrow{j}\]                                              \[|\overrightarrow{OC}|\ =10\ m.\]