A) 5
B) 1
C) 3
D) 4
Correct Answer: C
Solution :
Let \[{{v}_{r}}=\] velocity of river \[{{v}_{br}}=\]velocity of boat in still water and w = width of river Time taken to cross the river = 15 min \[=\frac{15}{60}h=\frac{1}{4}\,h\] Shortest path is taken when \[{{v}_{b}}\] is along AB. In this case \[v_{br}^{2}=v_{r}^{2}+v_{b}^{2}\] Now, \[t=\frac{w}{{{v}_{b}}}=\frac{w}{\sqrt{v_{br}^{2}-v_{r}^{2}}}\] \[\therefore \frac{1}{4}=\frac{1}{\sqrt{{{5}^{2}}-v_{r}^{2}}}\] \[\Rightarrow {{5}^{2}}-v_{r}^{2}=16\] \[\Rightarrow v_{r}^{2}=25-16=9\] \[\therefore {{v}_{r}}=\sqrt{9}\,=3\,km/h\] Note: If \[{{v}_{r}}\ge {{v}_{br}}\], the boatman can never reach at point B.You need to login to perform this action.
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