Question

A boat is sent across a river with a velocity of $3\text{km/h}$. If the resultant velocity of the boat is $5\text{km/h}$, then velocity of the river flow is

• A. $8\text{km/h}$
• B. $10\text{km/h}$
• C. $6\text{km/h}$
• D. $4\text{km/h}$

Answer 1

The correct option is D $4\text{km/h}$

From the relation we have
$\overrightarrow{v_{b,r}}=\overrightarrow{v_b}-\overrightarrow{v_r}...\left(i\right)$
given that velocity of boat w.r.t river is
$\overrightarrow{v_{b,r}}=3\text{km/h}\hat{j}$
Let the direction of river flow is along $+vex$ axis,
hence velocity of river w.r.t ground is $v_r\text{km/h}\hat{i}$

$\Rightarrow$ The velocity of boat w.r.t ground is
$\overrightarrow{v_b}=\overrightarrow{v_{b,r}}+\overrightarrow{v_r}$
$\overrightarrow{v_b}=3\hat{j}+v_r\hat{i}$
Hence resultant speed,
$|\overrightarrow{v_b}|=\sqrt{3^2+v_r^2}$,
given that $|\overrightarrow{v_b}|=5\text{km/h}$
$\Rightarrow 5^2=3^2+v_r^2$
$\Rightarrow v_r^2=25-9=16$
$\therefore v_r=\sqrt{16}=4\text{km/h}$