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. 1
• B. 3
• C. 4
• D. $\sqrt{41}$

Answer 1

The correct option is B 3

Resultant velocity of boat,
$V_m,r=\frac{1km}{15min}=4km{h}^{-1}$

${\overrightarrow{V}}_m,g={\overrightarrow{V}}_r,g+{\overrightarrow{V}}_m,r$
${\overrightarrow{V}}_r,g={\overrightarrow{V}}_m,g-{\overrightarrow{V}}_m,r$
$V_r,g=\sqrt{({\overrightarrow{V}}_m,g{)}^2-({\overrightarrow{V}}_m,r{)}^2}$
$V_r,g=\sqrt{5^2-4^2}=3km{h}^{-1}$