Question

A man crosses the river in minimum time of $10min$ with a drift of $120m.$ If he crosses the river in shortest path he takes $12.5min.$ What is his swimming speed?

• A. $20mmin^{- 1}$
• B. $15mmin^{- 1}$
• C. $10mmin^{- 1}$
• D. $5mmin^{- 1}$

Answer 1

Answer: (A)

For shortest time
$t_{1}=\frac{d}{v}=10\Rightarrow d=10v$
and $x=v_{R}t_{1}$
$120=v_{R}10$
$\Rightarrow v_{R}=12mmin^{- 1}$
For shortest path $t_{2}=\frac{d}{\sqrt{v^{2} - v_{R}^{2}}}$

$12.5=\frac{10 v}{\sqrt{v^{2} - 12^{2}}}\Rightarrow \sqrt{v^{2} - 12^{2}}=0.8v$
$v^{2}-12^{2}=0.64v^{2}$
$0.36v^{2}=144$
$v^{2}=400$
$v=20mmin^{- 1}$