Question

A swimmer wishes to cross a $1km$ wide river flowing at $5km{h}^{-1}$. his speed in still waters is $3km{h}^{-1}$. He has to reach directly opposite in minimum possible time. If he does not reach directly opposite by swimming, he has to walk that distance at $5km{h}^{-1}$. Find the time taken.

• A. $0.36hr$
• B. $0.66hr$
• C. $1hr$
• D. $1.36hr$

Answer 1

Answer: (B)

$0.66hr$

$let\theta betheanglebetweentherelativeveloctiyofboatandalineperpendiculartotheflow.timetakentocrosstheriver{t}_1=\frac{1}{3cos\theta }timetakentowhilewalking{t}_2=\frac{drift}{5}=\frac{1}{5}\left(\frac{5-3sin\theta }{3cos\theta }\right)totaltimet=\frac{1}{3cos\theta }+\frac{1}{5}\left(\frac{5-3sin\theta }{3cos\theta }\right)\frac{dt}{d\theta }=0\Rightarrow sin\theta =0.3\Rightarrow t=0.66hrs$