A swimmers velocity in still water is 4km/hr . He sets out at right angles to the bank of driver which is flowing at 3km/hr to swim across the river. What is his actual velocity through the water
Answers
Given : a swimmer whose velocity in still water is 4km/h sets out at right angles to the bank of a river which is flowing at 3km/h.
To Find : actual velocity through the water
Solution:
Let say final Velocity is V at angle α with bank of river
then Horizontal Velocity = VCosα = 3 km/hr river speed
Vertical Velocity = VSinα = 4 km/hr swimmer speed
(VCosα)² + ( VCosα )² = 3² + 4²
=> V²( Cos²α + Sin²α) = 9 + 16
=> V²( 1) = 25
=> V = 5
VSinα / VCosα = 4/3
=> tanα = 4/3
=> α = tan⁻¹( 4/3) = 53.13°
Velocity of 5 km/hr at an angle of 53.13° with bank of river
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