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Question

A river 800m wide flows at the rate of 5kmh−1 . A swimmer who can swim at 10kmh−1 in still water, wishes to cross the river straight.

(i) Along what direction must he strike?

(ii) What should be his resultant velocity?

(iii) How much time he would take?

(i) Along what direction must he strike?

(ii) What should be his resultant velocity?

(iii) How much time he would take?

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Solution

Let the angle between the swimmer and the perpendicular to the flow of river is θ with the perpendicular to the flow of river and time to cross the river is t

(i)

The direction is given as,

sinθ=510

θ=30∘

(ii)

The resultant velocity is given as,

V=Vsgcos30∘

=10cos30∘

=8.66km/h

(iii)

Displacement in vertical direction is given as,

(Vsgcosθ)t=800×10−3

(10cos30∘)t=800×10−3

t=0.092s

t=5.5min

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