Question

A person moves $30m$ north, from there $20m$ east and finally $30\sqrt{2}m$ south-west from there. His displacement from initial position is

• A. $10m$ west
• B. $10m$ east
• C. $5m$ west
• D. $5m$ east

Answer 1

The correct option is A $10m$ west

Consider the initial position is at the origin, and north is + Y axis, south being negative Y axis, east is positive X axis and west is negative X axis.
Then starting from origin, after moving $30m$ north, his coordinates become $(0,30)$.
Similarly, after $20m$ east, his coordinates are $(20,30)$
After $30\sqrt{2}m$ south west, (coordinates of the point 30 sqrt 2 metres south west from origin are $(-30,-30)$) the new coordinates of the person are $(-10,0)$.
So, his displacement from the initial position is $10m$ on the negative X axis, i.e., $10m$ west .