Question

A boat that has a speed of $5\text{km/hr}$ in still water crosses a river of width $1\text{km}$ along the shortest possible path in $20$ minutes. The velocity of the river water in $\left(\text{km/hr}\right)$ is

• A. $1$
• B. $3$
• C. $4$
• D. $4.5$

Answer 1

The correct option is C $4$

Displacement $=1\text{km}$
$t=\frac{20}{60}=\frac{1}{3}\text{hr}$

Velocity along $\text{AB}=\frac{\text{AB}}{t}$
i.e $v_{br}\cos \theta =\frac{1}{\frac{1}{3}}=3\text{km/hr}$
$\Rightarrow \cos \theta =\frac{3}{v_{br}}=\frac{3}{5}$
$\Rightarrow \sin \theta =\frac{4}{5}$


From triangle $\text{ABC}$,
$\sin \theta =\frac{v_r}{v_{br}}=\frac{v_r}{5}$
($\because$ Horizontal component of velocity of boat must become zero)
$\therefore v_r=4\text{km/hr}$