question_answer

The speed of a boat is 5 km/h in still water. If it crosses a river of" width 1 km along the shortest possible path in 15 min, then velocity of the river's water is :

A) 1 km/h                                 

B)  2 km/h

C)  3 km/h                                

D)   4 km/h

Correct Answer: C

Solution :

                 Key Idea: For shortest path velocity of boat must be perpendicular-to the river velocity. We know that, We know that, \[\text{Velocity = }\frac{\text{distance}}{\text{time}}\] Also, 1 h = 60 min \[\therefore \]     \[15\,,min\,=\frac{1}{4}\text{h}\] Now, relative velocity of boat is , \[{{v}_{b}}=\frac{d}{t}=\frac{1}{1/4}\,=4\,\text{km/h}\]                 Velocity of boat must be perpendicular to the velocity of river while crossing the river in shortest path. Hence, relation for velocity of river water is \[v_{br}^{2}=v_{b}^{2}+v_{w}^{2}\] \[\Rightarrow \]    \[{{5}^{2}}={{4}^{2}}=v_{w}^{2}\] \[\Rightarrow \]\[v_{w}^{2}=\sqrt{{{5}^{2}}-{{4}^{2}}}\,=3\,\text{km/h}\]