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

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.

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.