Question

A boat, which has a speed of $5km/h$ in still water, crosses a river of width $1km$ along the shortest possible path in $15\text{minutes}$. What is the magnitude of velocity of the river water?

• A. $5km/h$
• B. $4km/h$
• C. $3km/h$
• D. $6km/h$

Answer 1

The correct option is C $3km/h$

The speed of the boat in still water $=v_b=5km/h$
Width of the river $=s=1km$
Time taken $=t=15\text{minutes}=\frac{1}{4}h$
Speed of the boat w.r.t the river $=v_{br}=\frac{s}{t}=\frac{1}{\frac{1}{4}}=4km/h$
From the definition of relative velocity, we have
${\overrightarrow{v}}_{br}={\overrightarrow{v}}_b–{\overrightarrow{v}}_r$
Hence $|{\overrightarrow{v}}_{br}{|}^2=|{\overrightarrow{v}}_b{|}^2+|{\overrightarrow{v}}_r{|}^2\Rightarrow v_r=\sqrt{(5^2-4^2)}=3km/h$
Hence the correct option is (c).