A river is flowing from west to east direction with speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a

Question

A river is flowing from west to east direction with speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a boat capable of moving at a maximum speed of $27 \mathrm{~km} \mathrm{~h}^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of $150^{\circ}$ to direction of river flow, then the width of the river is\

Professor PC Thomas Classes · Answer

(a) : $\vec{V}_{R}=9 \hat{i} \mathrm{~km} / \mathrm{hr}$\ $V_{B / R}=27 \mathrm{~km} / \mathrm{hr}$\ $t=1 / 2 \mathrm{~min}$\  $\vec{V}_{B / R}=27\left(\cos 60^{\circ} \hat{j}-\sin 60^{\circ} \hat{i}ight)$\ $=27\left(-\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}ight)$\ $d=V_{B / R} \cos 60^{\circ} 	imes t=27 	imes \frac{1}{2} 	imes \frac{1}{2 	imes 60}$\ $=0.1125 \mathrm{~km}$\ $=112.5 \mathrm{~m}$\