Question

Ram moves in east direction at a speed of $6m/s$ and Shyam moves ${30}^o$ east of north at a speed of $6m/s$. The magnitude of their relative velocity is

• A. $3m/s$
• B. $6m/s$
• C. $6\sqrt{3}m/s$
• D. $6\sqrt{2}m/s$

Answer 1

The correct option is B $6m/s$

Given,

${\overrightarrow{v}}_r=6\hat{i}m/s$

${\overrightarrow{v}}_s=(6sin{30}^0\hat{i}+6cos{30}^0\hat{j})m/s$

${\overrightarrow{v}}_s=3\hat{i}+3\sqrt{3}\hat{j}$

Relative velocity is,

${\overrightarrow{v}}_{rs}={\overrightarrow{r}}_r-{\overrightarrow{v}}_s$

${\overrightarrow{v}}_{rs}=6\hat{i}-3\hat{i}-3\sqrt{3}\hat{j}$

${\overrightarrow{v}}_{rs}=3\hat{i}-3\sqrt{3}\hat{j}$

Magnitude, $|{\overrightarrow{v}}_{rs}|=\sqrt{3^2+(3\sqrt{3}{)}^2}=6m/s$

The correct option is B.