Question

A man wants to reach point B on the opposite bank
of a river flowing at a speed 4 m/s starting from A
as shown in figure. What minimum speed relative to
water should the man have so that he can reach
point B directly by swimming?
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Answer 1

ANSWER

Let v be the speed of boatman in still water.

Let v be the speed of boatman in still water.Resultant of v and u

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθ

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθ

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvy

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvyor 1=u−vsinθvcosθ

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvyor 1=u−vsinθvcosθ∴v=sinθ+cosθu

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvyor 1=u−vsinθvcosθ∴v=sinθ+cosθu=2sin(θ+45∘)u

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvyor 1=u−vsinθvcosθ∴v=sinθ+cosθu=2sin(θ+45∘)uv is minimum at, θ+45∘=90∘

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvyor 1=u−vsinθvcosθ∴v=sinθ+cosθu=2sin(θ+45∘)uv is minimum at, θ+45∘=90∘or θ+45∘

Let v be the speed of boatman in still water.Resultant of v and ushould be along AB. Components of vb(absolute velocity of boatman ) along x and y-direction are,vx=u−vsinθand vy=vcosθFurther, tan45∘=vxvyor 1=u−vsinθvcosθ∴v=sinθ+cosθu=2sin(θ+45∘)uv is minimum at, θ+45∘=90∘or θ+45∘and vmin=2u