Question

A boat which has a speed of $5km/h$ per hour in still water crosses a river of width $1km$ along the shortest possible path in $15\min$. The velocity of the river water (in $km/h$ ) is

Answer 1

Answer: 3

As shown in the figure, to cross the river along the shortest possible path, i.e, to make drift zero we have,
$v_{br}\sin \theta =v_r$ ...(i)
And time taken to cross the river will be
$t=\frac{d}{v_{br}\cos \theta }$ ....(ii)

From (ii), we have
$\frac{1}{4}=\frac{1}{5\cos \theta }$
$\Rightarrow \cos \theta =\frac{4}{5}$
Now, from (i), we have
$5\times \frac{3}{5}=v_r$
$\Rightarrow v_r=3km/h$