Kinematics 5

Wow, it's been long! :P

So, consider the following figure. The boat starts from point $A$ along the direction hinted by the arrow, at an angle $\theta$ with the river. Let the speed of the boat be given by ${v}_{b}$ and that of the river be given by ${v}_{r}$ .

As the boat crosses the river across the shortest path, so, its final journey must be along a straight line path from $A$ to $B$ , as shown in the figure. For this to be possible, a component of the boat's velocity must cancel the effect caused by the river. Therefore,

${v}_{b} \cos(\theta) = {v}_{r} \quad \quad (*)$

Also, time taken by boat to cover the width of the river gives us:

$\dfrac {1}{5\sin(\theta)} = 15 min. = 0.25 hr.$ $\Rightarrow \sin(\theta) = \dfrac {4}{5}$

So, $\cos(\theta) = \dfrac {3}{5}$ . Using this in $(*)$ , we get ${v}_{r} = 3 Km/hr$