# The impatient boatman

Classical Mechanics Level pending

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

×