question_answer

The speed of a boat is \[5\text{ }km/hr\] in still water. It crosses a river of width 1km along the shortest possible path in 15 minutes. The velocity of river water is

A)  \[\text{3 }km/hr\]   

B)  \[4\text{ }km/hr\]

C)  \[\text{5 }km/hr\]                   

D)  \[\text{2 }km/hr\]

Correct Answer: A

Solution :

 \[{{V}_{mr}}=5\,km/hr,\] \[t=15\,\min \] \[t=\frac{d}{\sqrt{V_{mr}^{2}-V_{r}^{2}}}\] \[\Rightarrow \]\[\frac{15}{60}=\frac{1}{\sqrt{25-V_{r}^{2}}}\] \[\Rightarrow \] \[4=\sqrt{25-V_{r}^{2}}\] \[\Rightarrow \]\[V_{r}^{2}=25-16\] \[\Rightarrow \]\[V_{r}^{2}=9\]\[\Rightarrow \] \[{{V}_{r}}=3\,km/hr\]