Question

A boat which has a speed of $5km/hr$ in still water crosses a river of width $1km$ along the shortest possible path in $20min$. The velocity of the river water in $km/hr$ is

• A. $1$
• B. $3$
• C. $4$
• D. $4.5$

Answer 1

The correct option is C $4$

Let $V_r$ be the magnitude of velocity of river and $V_b$ be the magnitude of velocity of boat in still water.
Displacement = $1km$
$t=\frac{20}{60}=\frac{1}{3}hr$

Velocity along $AB=\frac{AB}{t}$
$V_b\cos \left(\theta \right)=\frac{1}{\frac{1}{3}}=3km/hr$
From velocity triangle ABC,
$V_b^2=V_r^2+(V_b\cos \theta {)}^2$
$\Rightarrow V_r^2=V_b^2-(V_b\cos \theta {)}^2$
$\Rightarrow V_r^2=5^2-3^2=16$
$\Rightarrow V_r=4km/hr$