Question

A boat which has a speed of $5 \, km \, h^{- 1}$ in still water crosses a river of width $1 \, km$ along the shortest possible path in $15$ minutes. The velocity of the river water (in $km \, h^{- 1}$ ) is

• A. $3$
• B. $4$
• C. $\sqrt{21}$
• D. $1$

Answer 1

Answer: (A)

Speed along the shortest path ${l}\Rightarrow\left|\overrightarrow{\mathrm{v}}_{\mathrm{R}}\right|=\frac{\text { distance }}{\text { time }}=\frac{1}{\left(\frac{15}{60}\right)} \mathrm{km} \mathrm{h}^{-1} $
$\Rightarrow\left|\overrightarrow{\mathrm{v}}_{\mathrm{R}}\right|=4 \mathrm{~km} \mathrm{~h}^{-1}$
$\therefore \, $ Speed of water, $\overset{ \rightarrow }{\text{v}}_{water} \, = \, \sqrt{5^{2} - 4^{2}} \, = \, 3 \, km \, h^{- 1}$