A river `400 m` wide is flowing at a rate of `2.0 m//s.` A boat is sailing at a velocity of `10.0 m//s` with respect to the water In a direction perpendicular to the river.
(a) Find the time taken by the boat to reach the opposite bank.
(b) How far from the point directly opposite to the starting point does the boat reach the opposite bank?

Explanation

At III turn
Displacement `=vec(OA)+vec(AB)+vec(BC)=vec(OC)=500 cos 60^(@)+500+500 cos 60^(@)`
`=500xx1/2+500+500xx1/2=1000 m` from O to C
Distance `=500+500+500=1500 m`
So `("Displacement")/("Distance")=1000/1500=2/3`
At VI turn `:'` initial and final positions are same so displacement `=0`
and distance `=500xx6=3000 m`
`:. ("Displacement")/("Distance")=0/3000=0`
At VIII turn : Displacement `=2(500) cos (60^(@)/2)=1000xxcos 30^(@)=1000xxsqrt(3)/2=500sqrt(3) m`
Distance `=500xx8=4000 m :. ("Displacement")/("Distance")=(500sqrt(3))/4000=sqrt(3)/8`