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Question

A steamer plies between two stations A and B on opposite banks of a river, always following the path AB. The distance between stations A and B is 1200m. The velocity of the current is 17ms1 and is constant over the maim width of the river. The line AB makes an angle 60 with the direction of the flow. The steamer takes 5 min to cover the distance AB and back.
a. Find the velocity of steamer with respect to water.
b In what direction should the steamer move with respect to line AB?

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Solution

From A to B :AB=(vcosβ+ucosβ)t1
From B to A : AB=(ucosβucosα)t2
α60o,vsinβ=usinα
5×60=1200vcosβ+ucosα+1200vcosβucosα
putting u=17,α=60o,we get
v2cos2β8vcosβ174=0,vcosβ=172 ..............(ii)
from Eqs.(i) and (ii) , tanβ=317
β=tan1317 and v=85ms1

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