• # question_answer ) A man wants to reach point B on the opposite bank of a river flowing at a speed as shown in the figure. What minimum speed relative to water should the man have so that he can reach point B? A) $u\sqrt{2}$                            B) $\frac{u}{\sqrt{2}}$C) $2u$                            D) $\frac{u}{2}$

Let v be the speed of boatman in still water. Resultant of v and u should be along AB. Components of${{\vec{v}}_{b}}$(absolute velocity of boatman) along$x$and y Direction are, ${{v}_{x}}=u-v\sin \theta$ and ${{v}_{y}}=v\cos \theta$ Further, $\tan {{45}^{o}}=\frac{{{v}_{y}}}{{{v}_{x}}}$ or $1=\frac{v\cos \theta }{u-v\sin \theta }$ $v=\frac{u}{\sin \theta +\cos \theta }=\frac{u}{\sqrt{2}\sin (\theta +{{45}^{o}})}$ v is minimum at, $\theta +{{45}^{o}}={{90}^{o}}$or $\theta ={{45}^{o}}$ and ${{v}_{\min }}=\frac{u}{\sqrt{2}}$