Question

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

Answer 1

As shown in the figure, to cross the river along the shortest possible path, i.e, to make drift zero we have,
$v_{b r} \sin \theta=v_{r}$ ...(i)
And time taken to cross the river will be
$t=\frac{d}{v_{b r} \cos \theta}$ ....(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} $
$\Rightarrow v_{r}=3\, km / h$