Question

a boat moves relative to water with velocity 10 km per hour the velocity of river flows is 5 km per hour at what angle to the stream direction must the boat move to minimise drifting
please give a descriptive answer​

Answer 1

Let the velocity of boat is v and making an angle θ with the vertical and the width of the river is d. Then the velocity of river is 2v in horizontal direction.

The resultant velocity of boat is given as,

v

x

=2v−vsinθ

v

y

=vcosθ

The required time to cross the river is given as,

t=

vcosθ

d

The drift is given as,

x=v

x

×t

x=2v−vsinθ×

vcosθ

d

For drift to be minimum,

dθ

dx

=0

2vtanθ−vsecθ=0

θ=30

∘

The angle made with the direction of river flow is given as,

θ

1

=90

∘

+30

∘

θ

1

=120

∘

The value of n is given as,

n

2π

=120

∘

n=3

hope this helps

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