Question

A boatman can row with a speed of $10km{h}^{-1}$ in still water. River flows at $6km{h}^{-1}$. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross that river of width $1km$ is

• A. $\frac{1}{8}h$
• B. $\frac{1}{4}h$
• C. $\frac{1}{2}h$
• D. $1h$

Answer 1

Answer: (A)

Refer figure. The boatman can cross the river along the shortest possible path if the resultant velocity $\vec{v}$ of boatman ${\vec{v}}_b$ and river velocity ${\vec{v}}_r$ is along $\overrightarrow{OC}$. It will be so if the boatman goes along $\overrightarrow{OB}$. Then
$v=\sqrt{v_b^2-v_r^2}=\sqrt{10^2-6^2}=8km{h}^{-1}$
Time taken to cross the river,
$t=\frac{1km}{8km{h}^{-1}}=\frac{1}{8}h$