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

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????

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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

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