A boat moves relative to water with a velocity which is n=2.0 times less than the river flow velocity. The angle (in degrees) to the stream direction must the boat move to minimize drifting is (120+x) . The value of x is :
Let v0 be the stream velocity and v′ the velocity of boat with respect to water. At
v0v′=η=2>0, some drifting of boat is inevitable.
Let →v′ make an angle θ with flow direction (shown in figure below), then the time taken to cross the river
t=dv′sinθ (where d is the width of the river)
In this time interval, the drifting of the boat
x=(v′cosθ+v0)t
=(v′cosθ+v0)dv′sinθ=(cotθ+ηcscθ)d
For xmin (minimum drifting)
ddθ(cotθ+ηcscθ)=0, which yields
cosθ=−1η=−12
Hence, θ=120∘