question_answer

The speed of boat is 5 km/h in still water. It crosses a river of width 1 km along the shortest possible path in 15 min. Then velocity of river will be:

A) 4.5 km/h                             

B) 1 km/h

C) 1.5 km/h                             

D) 3 km/h

Correct Answer: D

Solution :

Time taken to cross the river by shortest path = 15 min. \[\because \]  \[60\,\min =1\,\text{h}\] \[\because \]   \[15\,\min =\frac{1}{60}\times 15\,\text{h =}\frac{1}{4}\,\text{h}\] \[\text{Velocity =}\frac{\text{distance}}{\text{time}}=\frac{1}{1/4}=4\,km/h\] or                   \[{{v}_{br}}=5\,\text{km/h}\] Velocity of river is given by \[v=\sqrt{{{(5)}^{2}}-{{(4)}^{2}}}=3\,\text{km/h}\]