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# Solve it

Asked by hariom2083 22nd July 2018, 12:18 PM

(Vectors are typed Bold letters)

Let u is velocity of water and v is velocity of swimmer.

swimmer is moving along the line AC , which gives the direction u+v.
The resultant vector makes an angle θ with horizontal which is given as tanθ = d/120 , where d is width of river.

when the swimmer is moving along the line AC, he is reaching the point C in 10 minutes, so we have

when the swimmer moves in a direction that makes an angle α with the width of river as shown in figure,
he crosses the river in 12.5 minutes,
hence if we resolve v along the direction paralle to river speed and perpendicule to river speed,  we have

from eqns. (1) and (2), we get

we arrived the equations for river velocity and swimmer velocity in terms of width of river.
We can proceed further to find river speed and width of river by method of elimination using
the list of answers given for river speed and width of river.

It means, we substitute value for d from the list of values given in Q2 list and get u from eqn.(3).

If the calcultaed u-value matches with one of the u-values given in the list,
then we conclude that respective d and u values are the required answer.

when I did the calculations for d=200 m I got u = 0.72 kmph.

Hence the answer is :- (a) river speed 0.72 km/h  (b) width of the river = 200 m

Answered by Expert 26th July 2018, 3:25 PM
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Tags: time speed