Question

Three ships $A,B\&C$ are in motion. The motion of $A$ as seen by $B$ is with speed $v$ towards north-east. The motion of $B$ as seen by $C$ is with speed $v$ towards the north - west. Then as seen by $A,C$ will be moving towards

• A. north
• B. south
• C. east
• D. west

Answer 1

Answer: (B)

${\vec{v}}_A-{\vec{v}}_B=v\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right);{\vec{v}}_B-{\vec{v}}_c\left(\frac{-\hat{i}+\hat{j}}{\sqrt{2}}\right)$

Adding:

$\Rightarrow {\vec{v}}_A-{\vec{v}}_c=\frac{2v}{\sqrt{2}}\hat{j}$

$\Rightarrow {\vec{v}}_c-{\vec{v}}_A=-\sqrt{2}v\hat{j}=\sqrt{2}\left(-\hat{j}\right)$

So C will be moving towards south as seen by A.

or $a_p>10m/s^2$