The width of a river is $2.4 \mathrm{~km}$. The velocity of a boat in still water is $13 \mathrm{~km

Question

The width of a river is $2.4 \mathrm{~km}$. The velocity of a boat in still water is $13 \mathrm{~km} / \mathrm{hr}$. The boat covered the width of the river in the shortest time of $12 \mathrm{~min}$. Then the velocity of the river stream is

Professor PC Thomas Classes · Answer

(a) : For the shortest time path, the resultant velocity $v_{	ext{Resultant}} = \frac{	ext{width}}{	ext{time}} = \frac{2.4 \mathrm{~km}}{12/60 \mathrm{~hr}} = \frac{2.4}{0.2} = 12 \mathrm{~km} / \mathrm{hr}$. \ Here, $v_{	ext{Boat}} = 13 \mathrm{~km} / \mathrm{hr}$. By vector addition, $v_{	ext{River}} = \sqrt{v_{	ext{Boat}}^2 - v_{	ext{Resultant}}^2} = \sqrt{13^2 - 12^2} = 5 \mathrm{~km} / \mathrm{hr}$.