Question

A swimmer who can swim in a river with speed $\alpha V$ (with respect to still water) where $V$ is the velocity of river current, jumps into the river from one bank to cross the river.

• A. If $\alpha <1$ he can not cross the river
• B. If $\alpha \le 1,$ he can not reach a point on other bank directly opposite to his starting point.
• C. If $\alpha >1,$ he can reach a point on other bank directly opposite to his starting point.
• D. He can reach the other bank at some point, for any non zero value of $\alpha$

Answer 1

Answer: (B), (C), (D)

He can reach the other bank at some point, for any non zero value of $\alpha$

Given, Drift $=0$
Now, from figure
Drift $=(V-\alpha V\sin \theta )t=0$
$\Rightarrow \sin \theta =\frac{1}{\alpha }<1$


$\therefore$ For $\alpha >1$, the swimmer can reach the other bank with zero drift.
For other values of $\alpha$ the swimmer reaches the other bank but with non-zero drift.