Question

A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift of 120 m. If he crosses the river taking shortest route, he takes 12.5 minutes, find velocity of the boat with respect to water.

• A. $12m/min$
• B. $20m/min$
• C. $5m/min$
• D. $31m/min$

Answer 1

The correct option is B

$20m/min$

Case - 1: If man cross the river in minimum time he should move perpendicular to bank or normal to the

direction of water flow.

Man crossing river taking

minimum time

Let $|{\overrightarrow{v}}_{m,w}|=v;|{\overrightarrow{v}}_w|=u$

Time to cross river $t_1$ = 10 = $\frac{d}{v}\Rightarrow d=10v$
Drift, $x=u{t}_1\Rightarrow 120=u\times 10\Rightarrow u=12m/min$

Case - 2:
If man cross river taking shortest route, the drift should be zero.

Man crossing river taking

shortest route

Time to cross river $t_2=12.5=\frac{d}{\sqrt{v^2-u^2}}$

From case-1,
$d=10v$ and $u=12m/min$; $12.5=\frac{10v}{\sqrt{v^2-{12}^2}}\Rightarrow v=20m/min$