Question

A boat is rowed perpendicular to river flow at the rate of $4.5\text{km/hr}$. The river flows at the rate of $6\text{km/hr}$. The speed of boat in $\text{m/s}$ is

• A. $3.1$
• B. $2.1$
• C. $2.9$
• D. $5$

Answer 1

The correct option is B $2.1$

Velocity of boat w.r.t river, ${\overrightarrow{V}}_{b,r}=4.5\hat{j}\text{km/hr}$
Velocity of river w.r.t ground,${\overrightarrow{V}}_{r,g}=6\hat{i}\text{km/hr}$
Velocity of boat w.r.t ground $={\overrightarrow{V}}_{b,g}$
Since,
${\overrightarrow{V}}_{b,r}={\overrightarrow{V}}_{b,g}-{\overrightarrow{V}}_{r,g}$
$\Rightarrow {\overrightarrow{V}}_{b,g}={\overrightarrow{V}}_{b,r}+{\overrightarrow{V}}_{r,g}$
$\Rightarrow {\overrightarrow{V}}_{b,g}=(4.5\hat{j}+6\hat{i})=(6\hat{i}+4.5\hat{j})\text{km/hr}$
$|{\overrightarrow{V}}_{b,g}|=\sqrt{6^2+{4.5}^2}\times \frac{5}{18}=7.5\times \frac{5}{18}=\frac{37.5}{18}=2.1\text{m/sec}$