Question

Example 12. A river 800 m wide flows at the rate of
5 kmh-1. A swimmer who can swim at 10 kmh-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 ?
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Answer 1

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In order to find the values, let's assume that the ∠ between the swimmer and the perpendicular to the flow of river is θ.

Now, we'll directly substitute the values in formula's.

I) We know that,

Direction is given by :

→ Sinθ = rate of river /rate at which swimmer swims

→ Sinθ = 5/10

→ Sinθ = 1/2

→ Sinθ = 30°

II) Resultant velocity is given by :

↬V = Vswimmer × cosθ

↬V = 10 × cos30°

↬V = 8.67 km/h

III) Displacement in vertical direction is given by :

→ Vswimmer Cosθ × t = 800 × $10^-3$

→ 10 × cos30° × t = 800 × $10^-3$

→ t = 0.092 sec

→ t = 5.5 min