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 $