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????

Dear aruka

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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