Question

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

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

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 $\overrightarrow{O C}$. It will be so if the boatman goes along $\overrightarrow{O B}$. Then
$v=\sqrt{v_{b}^{2}-v_{r}^{2}}=\sqrt{10^{2}-6^{2}}=8 km h ^{-1}$
Time taken to cross the river,
$t=\frac{1 km }{8 km h ^{-1}}=\frac{1}{8} h$