A boat is moving towards east with a velocity 4m/s with respect to still water and the river is flowing towards north with velocity 2m/s and the wind is blowing towards north witg velocity 6m/s determine the direction of flag blown over by the wind hoisted on the boat

Refer to the figure below.

The velocity diagram adds the speed of the boat (due east) as a vector to the combined speed of the water and the wind (due north) to obtain the velocity of the flag, at an angle θ, counterclockwise from the eastern direction.

By definition,

tan θ = 8/4 = 2

θ = arctan (2) = 63.4°

Answer:

The flag blows in a direction which is 63.4° measured counterclockwise from the eastern direction.