There is a river of width 'd' km,on one side of which is an impatient boatman B,who wants to reach the lighthouse L which is exactly opposite him and'd' km further from the opposite bank as shown in the figure.

So he hires a speedboat which has speed'\({ v }_{ B }\)'(in still water) equal to that of the river '\({ v }_{ r }\) ' .

He reckons that to reach there in the shortest time , his boat should always point towards the lighthouse.He reaches the opposite bank at D.

Find distance CD(in km).

Details and Assumptions

\(\rightarrow\) \( { v }_{ r }\)=5 km/hr

\(\rightarrow\) d=1km

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