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araku valley Grade:
        

how to find the shortest path travelled by a boatman ,when,VELOCITY OF THE RIVER "vR" IS GREATER THAN THE VELOCITY OF THE BOATMAN W.R.T THE RIVER "vBR".(vR>vBR).


MY BOOK SAYS TO TAKE "dx/dΦ=0" {x=min displ.,Φ=angle w.r.t y-axis}.BUT I DO NOT UNDERSTAND THE PURPOSE OF IT.IS IT DUE TO MAXIMA AND MINIMA????

6 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear aruka


 


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consider the situation as given in diagram


time taken to cross the river is t=d/vcosΘ


so distance AC =(u-vcosΘ)t


                     = (u-vcosΘ)d/vcosΘ


 


so distance travel  OC =x =[d2 +  {(u-vcosΘ)d/vcosΘ}2]1/2


so distance travel is dependent upon the angel   Θ  ,so for minimum value of x differentiate x w.r.t Θ


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Badiuddin

6 years ago
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