Question

A boat goes across a river in shortest possible time with a velocity $12km/h$ . The magnitude of its resultant speed in flowing water is $13km/h$. The magnitude of velocity of water flow in the river is

• A. $5km/h$
• B. $7km/h$
• C. $9km/h$
• D. $1km/h$

Answer 1

The correct option is A $5km/h$

Let ${\overrightarrow{V}}_{br}$ be the velocity of boat w.r.t river and ${\overrightarrow{V}}_r$ be the velocity of water flow in river.
According to question,
${\overrightarrow{V}}_{br}=12km/h$ ($\overrightarrow{V_{br}}$ is perpendicular to the flow of the river for shortest time)
and
Velocity of boat w.r.t ground, ${\overrightarrow{V}}_b=13km/h$
We know that
${\overrightarrow{V}}_{br}={\overrightarrow{V}}_b-{\overrightarrow{V}}_r\Rightarrow {\overrightarrow{V}}_b={\overrightarrow{V}}_{br}+{\overrightarrow{V}}_r{V}_b=\sqrt{V_{br}^2+V_r^2}$
$V_b=\sqrt{{12}^2+V_r^2}$
$13=\sqrt{144+V_r^2}$
$V_r^2=25\Rightarrow V_r=5km/h$