Question

To the captain of a ship 𝐴 travelling with velocity $\overrightarrow{A}=(3\hat{i}-4\hat{j})km/hr$ , a second ship $B$ appears to have a velocity $(5\hat{i}+12\hat{j})km/hr$. What is the true velocity of the ship $B$ ?

• A. $(-2\hat{i}-16\hat{j})km/hr$
• B. $8(\hat{i}+\hat{j})km/hr$
• C. $(13\hat{i}+8\hat{j})km/hr$
• D. $(2\hat{i}+16\hat{j})km/hr$

Answer 1

The correct option is B $8(\hat{i}+\hat{j})km/hr$

Given,
${\overrightarrow{V}}_A=(3\hat{i}-4\hat{j})km/hr$
${\overrightarrow{V}}_{BA}=(5\hat{i}+12\hat{j})km/hr$
True velocity of $B$:
${\overrightarrow{V}}_B={\overrightarrow{V}}_A+{\overrightarrow{V}}_{BA}$
$=3\hat{i}-4\hat{j}+5\hat{i}+12\hat{j}$
$=(8\hat{i}+8\hat{j})km/hr$
Final Answer: (d)