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 $a_{p} > 10 \,m/s^2$