Question

A particle $A$ is moving towards North with an acceleration of $5{ms}^{-2}$ and particle $B$ is moving North-East direction with an acceleration of $5\sqrt{2}{ms}^{-2}$. Find relative acceleration of particle $A$ with respect to particle $B$.

Answer 1

On considering east as positive x-axis and north as positive y-axis.

We have, Acceleration of A $=5\hat{j}$ and Acceleration of B $=5\sqrt{2}\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

Now, relative acceleration of particleA wrt particle B $=\left({\overrightarrow{a}}_{AB}\right)={\overrightarrow{a}}_A-{\overrightarrow{a}}_B$

$=5\hat{j}$ $-5\sqrt{2}\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

$=-5\hat{i}$

So, relative acceleration is $5m/s^2$ towards west.