Question

A ship $\text{A}$ sailing due east with a absolute velocity of $10\text{km/h}$, which appears to be sailing due north with a velocity of $5\text{km/h}$, to a person, sitting in a moving ship $\text{B}$. Determine the velocity (absolute) of ship $\text{B}$.

• A. $5\sqrt{5}\text{km/h}$
• B. $5\sqrt{6}\text{km/h}$
• C. $4\sqrt{5}\text{km/h}$
• D. $4\sqrt{6}\text{km/h}$

Answer 1

The correct option is A $5\sqrt{5}\text{km/h}$

Here we are given velocity of '$A$' ${\overrightarrow{v}}_A=10\hat{i}$

Velocity of $A$ w.r.t $B$, $v_{A/B}=5\hat{j}$
We know that, $v_{A/B}=v_A-v_B$
$\Rightarrow 5\hat{j}=10\hat{i}-v_B$

$\Rightarrow v_B=10\hat{i}-5\hat{j}$

Hence magnitude of absolute velocity of B is ,
$|v_B|=\sqrt{{10}^2+5^2}=5\sqrt{5}\text{kmph}$