Question

A man who can swim at a speed $v$ relative to the water wants to cross a river of width $d$, flowing with a speed $u$.The point opposite him across the river is $P$.

• A. The minimum time in which he can cross the river is $\frac{d}{v}$
• B. He can reach the point $P$ in time $\frac{d}{v}$.
• C. He can reach the point in time $\frac{d}{\sqrt{v^2-u^2}}$
• D. He cannot reach $P$ if $u>v$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A The minimum time in which he can cross the river is $\frac{d}{v}$
C He can reach the point in time $\frac{d}{\sqrt{v^2-u^2}}$
D He cannot reach $P$ if $u>v$.

Minimum time is when the man moves perpendicular to flow of river. If he has to reach point P then his velocity perpendicular to the flow of river is $\sqrt{v^2-u^2}$, so he can reach in time $d/\sqrt{v^2-u^2}$. If the river velocity is more than the relative velocity of man then his velocity can never be zero in the direction of flow and thus, he cannot reach point P.