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About which has a speed of 5km/h in still water crosses a river of width 1km along the shortest possible path in 15minutes.the velocity of the river water(in km/h) is- About which has a speed of 5km/h in still water crosses a river of width 1km along the shortest possible path in 15minutes.the velocity of the river water(in km/h) is-
Let the velocity of the river be 'v' along C to B and the boat is rowed along A to C so that the resultant velocity of the boat rows it along A to B For the boat to take the shortest distance, it should reach the point directly opposite to the width of the river that is B For that, the boat should be rowed at an angle against the flow of river along A to C so that the boat covers the 1km distance with the resultant velocity **********B***x km***C************** **********!************/**************... **********!***********/***************... **********!**********/****************... **********!*********/*****************... **********!********/******************... **1 km**!*******/**y km************* **********!******/********************... **********!*****/*********************... **********!****/**********************... **********!***/***********************... **********!**/************************... **********!*/*************************... **********A*************************** A to B: Distance = 1 km Velocity of the boat is the resultant of boat's velocity in still water and river's velocity A to C: Distance = y km Speed of the boat = 5km/hr C to B: Distance = x km (Drift of the boat due to river's velocity) Speed of the river = v km/hr Time in both cases = 15/60 hr = 1/4 = y/5 = x/v So, y=5/4 and x=v/4 In right triangle ABC, AB^2 + BC^2 = AC^2 x^2 + 1^2 = y^2 (v/4)^2 + 1 = (5/4)^2 v = 3 km/hr = velocity of river along C to B OR THE QUESTION CAN BE SIMPLY SOLVED AS FOLLOWS: In still water, Distance=1km Speed , s=5km/hr So, Time taken = 1/5 hr In the flowing river, Distance = 1km as the boat is supposed to take the shortest route (directly opposite) Time = 15 min = 15/60hr =1/4 hr Resultant speed of boat in river , u = 1/(1/4) = 4 km/hr Let the speed of river be v Using pythagoras theorem in the velocity triangle u^2=s^2-v^2 4^2=5^2-v^2 v=3km/hr
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