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a boat having a speed of 5km/hr . in still water crossing a river of width 1km long the shortest possible paths in 15 min the speed of the river in km/ hr
Asked by kishorantarkar26 | 05 Sep, 2023, 02:58: AM
Expert Answer
Vector diagram showing velocity of boat and velocity of river are shown above.
u is velocity of boat so that direction of velocit of boat u makes angle θ with the line parallel to width of river.
ur is velocity of river.
magnitude of velocity of boat , u = 5 km / hr = 5 × ( 5 / 18) m/s = ( 25/18 ) m/s
velocity component along the line parallel to width of river = u cosθ .
If boat travels along shortest path to cross the river and time taken to cross the river is 15 min ,
then we have
If we substitute u = ( 25/18 ) m/s , then we get
From above expression we get , cosθ = 0.8
Hence , sinθ = 
From vector diagram, we see that
Hence, speed of river = (5/6) × (18/5) km/hr = 3 km/hr
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