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# 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 $6m/s$.

Last updated date: 15th Jul 2024
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Hint: 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.

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.