Question

A boat man can row with a speed of 10 km/h in still water. If the river flows at 5 km/h, the direction in which the boat man should row to reach a point on the other bank directly opposite to the point from where he started is (width of the river is 2 km):

• A. in a direction inclined at $120{}^{\circ }$ to the direction of river flow
• B. in a direction inclined at $90{}^{\circ }$ to the direction of river flow
• C. $60{}^{\circ }$ in the north-west direction
• D. should row directly along the river flow
• E. none of the above

Answer 1

Answer: (A)

$\sin \theta =\frac{CB}{AC}=\frac{5}{10}=\frac{1}{2}\Rightarrow \theta =30{}^{\circ }$
$\therefore$ $\theta =180{}^{\circ }-\angle ACB$ $=180{}^{\circ }-[180{}^{\circ }-(90{}^{\circ }+30{}^{\circ })]$ $=180{}^{\circ }-60{}^{\circ }=120{}^{\circ }$