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