Question

A person travels $20m$ East, $8m$ North and finally $8\sqrt{2}$ North-West. Find the displacement of person?

• A. $\sqrt{284}m$
• B. $\sqrt{298}m$
• C. $\sqrt{300}m$
• D. $\sqrt{400}m$

Answer 1

The correct option is D $\sqrt{400}m$

Towards north is $X_N=8m$ and towards east is $X_E=20m$

Now the $8\sqrt{2}m$ towards North-west can be $rewritten$ as $8\times \sqrt{2}(\frac{1}{\sqrt{2}}North+\frac{1}{\sqrt{2}}West)=8mNorth+8mWest$

so the net displacement in east will be $X_E-8m=12m$

so the net displacement in North will be $X_N+8m=16m$

now we have to calculate its $vector$ sum as $North$ and $EAST$ are $perpendicular$ to each other so net

displacement will be $d=\sqrt{{12}^2+{16}^2}=20m$