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 $15$ minutes. The velocity of the river water is

• A. $2km/hr$
• B. $4km/hr$
• C. $3km/hr$
• D. $5km/hr$

Answer 1

The correct option is C $3km/hr$

The boat crosses the river by the shortest path if it moves perpendicular to the river current.


Referring to the figure, let $\overrightarrow{V_b}$ and $\overrightarrow{V_r}$ be the velocities of the boat and the river water w.r.t the ground. The velocity of the boat in still water is equal to the relative velocity of the boat w.r.t water i.e.
$\overrightarrow{V_{br}}=\overrightarrow{V_b}-\overrightarrow{V_r}$
which gives, ${\left|\overrightarrow{V_{br}}\right|}^2={\left|\overrightarrow{V_b}\right|}^2+{\left|\overrightarrow{V_r}\right|}^2$ .....(i)
($\because \overrightarrow{V_b}\perp \overrightarrow{V_r})$
Given, speed of the boat in still water $\left|\overrightarrow{V_{br}}\right|=5km/hr$ and the speed of the boat relative to the ground is,
$\left|\overrightarrow{V_b}\right|=\frac{\text{Width of the river}}{\text{Time taken}}=\frac{1}{\frac{15}{60}}=4km/hr$
Putting both the values in (i) we will get, $\left|\overrightarrow{V_r}\right|=3km/hr$