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A boat moves relative to water with a velocity which is n times less than the river flow velocity. At angle of the stream direction must the boat move to minimise drifting? |
Answer» SOLUTION :in thisproblem. Onethingshouldbe carefullynotedofboatis lessthanthe riverflowvelocity. Insucha CASE, boatcannotreachthe pointdirectlyoppositeto itsstartingpointi.e.,driftcanneverbezero , thustominimizethedriftboatstartat anangle` theta ` fromnormaldirectionupsterm asshown  Nowagainif wefindthe COMPONENTSOF velocityof boatand perpendiculartotheflowthesearevelocityalongtheriver` V_t= u - V sintheta` andvelocityperpendicularto theriver`,V_y= v costheta ` timetakento crosstheriveris`t= ( d )/( v_y)= (d )/( cos theta)` In thistimedrift` X=(v_A) t= ( u-v sintheta) (d)/(v_y) =(d)/(v costheta)` in thistimedrift`x =( v_x)t=( u- V sintheta ) (d)/( vcos theta) (or) x= (ud )/( v )sec theta-dtantheta ` the driftx isminimumwhen `( dx )/(d theta ) =0(or)( (ud)/(v)) ( sectheta, tantheta)- dsec^2theta =0` ` (or)(a)/(v )sin theta=1(or) sin theta= ( v )/( u )= (1 )/(n)( asv=(u )/(n))` sofor minimumdriftthe boatmustmoveat an angle` theta= sin ^(-1)((v)/( u ))`fromnormaldireactionor anangle`(pi)/(2)+ sin ^(-1) ((v)/(u ))`fromsteamdirection. |
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