A boat can move in river water with speed of 8km/h. This boat has to reach to a place from one bank of the river to a place which is in perpendicular direction on the other bank of the river. Then (i) in which direction should the boat  has to  be moved ? (ii) If the width of the  river is 600m; then what will be the time taken by the boat to cross the river ? The river flows with velocity 4km/h.

Velocity of man w.r.t. river is = Vm, r

Velocity of river w.r.t. ground is = Vr, g

Velocity of man w.r.t. ground is = Vm, g

Given,

|Vm, r| = 8 km/h

|Vr, g| = 4 km/h

Width of river = 600 m = 0.6 km

Since, the swimmer has to reach the opposite point in the other bank, so,

Vm, r cosθ + Vr, g = 0

=> 8 cosθ + 4 = 0

=> cosθ = -½

=> θ = 1200

Now,

Vm, g = [(Vm, r)2 + (Vr, g)2 + 2(Vm, r)(Vr, g)(cos120)]1/2

=> Vm, g = [82 + 42 + 2(8)(4)(-1/2)]1/2 = [80 - 32]1/2

=> Vm, g = 4√3 km/h

With this speed it has to travel 0.6 km.

So, time taken is = 0.6/(4√3) = 0.087 h = 5.2 minutes

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