Question

A boat man could row his boat with a speed $10\text{m/sec}$. He wants to take his boat from $P$ to a point $Q$ just opposite on the other bank of the river flowing at a speed $4\text{m/sec}$. He should row his boat–

• A. At right angle to the stream
• B. At an angle of ${\sin }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ up the stream
• C. At an angle of ${\sin }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ down the stream
• D. At an angle of ${\cos }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ down the stream

Answer 1

The correct option is B At an angle of ${\sin }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ up the stream


Let $v_b$ be the velocity of the boat w.r.t. the river
$\sin \theta =\frac{v_s}{v_b}$
$\theta ={\sin }^{-1}\left(\frac{4}{10}\right)$
$\theta ={\sin }^{-1}\left(\frac{2}{5}\right)$ with $PQ$ up the stream.