Question

A boat is moving towards east with velocity $4m/s$ wrt still water and river is flowing towards north with velocity $2m/s$ and the wind is blowing towards north with velocity $6m/s$.

Answer 1

We will try to understand the question first then arrange each data one by one and finally by applying $6m/s$ and many other formulas along with this we will get the accurate answer.

Complete answer:
The velocity of boat with respect to river or Vbr$= 4 \uparrow .$ Let us assume that East is our X axis is North is our Y axis. Velocity or river or ${V_r} = 2 \uparrow$
Here,

$${V_b} = 2 \uparrow + 4J \\\ \overrightarrow {{V_b}_r} = {\overrightarrow V _b} - \overrightarrow {{V_r}} \\\ \overrightarrow {{V_b}} = \overrightarrow {{V_{br}}} + \overrightarrow {{V_r}} \\\$$

Velocity of wind $\left( {{V_w}} \right) = 6J$
Velocity of wind with respect to the boat is referred as $\left( {{V_{wb}}} \right)$

$$\therefore \overrightarrow {{V_{wb}}} = \overrightarrow {{V_w}} - \overrightarrow {{V_b}} \\\ = 6J - \left( {2 \uparrow + 4J} \right) \\\ = - 2 \uparrow + 2J \\\$$

$\therefore$Direction of the flag is in the North West.
Hence, the correct answer is North West direction.

Note: Boat velocity is $4m/s$ towards east is $4J$. Velocity of wind is $6m/s$. To solve the other boat problems, we need to understand other many formulas for eg: The speed of a boat relative to the water is equal to the speed of the boat in still water.