Question

A boat is rowed perpendicular to river flow at the rate of $5\text{km/hr}$. The river flows at the rate of $2.5\text{km/hr}$. The speed of boat approximately in $\text{m/s}$ is

• A. $3\text{m/sec}$
• B. $2.5\text{m/sec}$
• C. $1.5\text{m/sec}$
• D. $3.6\text{m/sec}$

Answer 1

The correct option is C $1.5\text{m/sec}$

Velocity of boat w.r.t river, ${\overrightarrow{V}}_{b,r}=5\hat{j}\text{km/hr}$
Velocity of river w.r.t ground,${\overrightarrow{V}}_{r,g}=2.5\hat{i}\text{km/hr}$
Velocity of boat w.r.t ground $={\overrightarrow{V}}_{b,g}$
Since,
${\overrightarrow{V}}_{b,r}={\overrightarrow{V}}_{b,g}-{\overrightarrow{V}}_{r,g}$
$\Rightarrow {\overrightarrow{V}}_{b,g}={\overrightarrow{V}}_{b,r}+{\overrightarrow{V}}_{r,g}$
$\Rightarrow {\overrightarrow{V}}_{b,g}=(5\hat{j}+2.5\hat{i})=(2.5\hat{i}+5\hat{j})\text{km/hr}$
$|{\overrightarrow{V}}_{b,g}|=\sqrt{{2.5}^2+5^2}\times \frac{5}{18}\approx 5.6\times \frac{5}{18}=\frac{28}{18}=1.56\text{m/sec}$