Kinematics Question 119
Question: 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]
Options:
A) 10 m along north
B) 10 m long south
C) 10 m along west
D) Zero
Show Answer
Answer:
Correct Answer: C
Solution:
$ \overrightarrow{OA}=0\ \overrightarrow{i}+30\ \overrightarrow{j} $ , $ \overrightarrow{AB}=20\ \overrightarrow{i}+0\ \overrightarrow{j} $
$ \overrightarrow{BC}=-30\sqrt{2}\ cos45^{o}\overrightarrow{i} $
$ -30\sqrt{2}\ \sin 4{{5}^{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. $
