A boatman wants to reach from one bank of a 2km wide river to a point on another bank , directly opposite to the point from where he started . If he rows with a speed of 8 km/h , in still water and river flows at the rate of `14km//he`, in which direction he should row ?

Explanation

The boatman start from A and should reach B. The river flow is along DB, so he should row along AD.
Here, `AvecD=vecv_(m)=8km//hr`
Here , `AvecB` is the resultant of `AvecD and vecB`.
`angle BAD=beta and angle DBA=90^(@)`n
Since A and B are directly opposite,
`sin beta=(DB)/(AD)=(v_(R))/(u_(m))=(4)/(8)=(1)/(2)`
`rArr beta =30^(@)`
`therefore theta=90^(@) +30^(@)=120^(@)`
So, the boatman should row the boat in the direction at an angle of `120^(@)` with river flow.