Question

A flag on a boat at rest is fluttering in the south-east direction when the wind is blowing at a speed of \(72\) kmph. If the boat starts moving towards south with a speed of \(36\sqrt2\) kmph, then the direction of the flag on the boat is:

• A. South
• B. West
• C. North
• D. East

Hint:

For moving observers: \[ \vec V_{relative} = \vec V_{wind} - \vec V_{observer}. \] The flag always aligns with the relative wind.

Answer 1

The Correct Option is D

Concept: The flag aligns along the direction of the relative velocity of wind with respect to the boat. \[ \vec V_{WB} = \vec V_W-\vec V_B. \]

Step 1: Resolve wind velocity.
Wind blows toward south-east. Thus, \[ V_x=\frac{72}{\sqrt2}=36\sqrt2 \] towards east. \[ V_y=\frac{72}{\sqrt2}=36\sqrt2 \] towards south.

Step 2: Write boat velocity.
Boat moves south with velocity \[ 36\sqrt2. \] Thus \[ \vec V_B=(0,36\sqrt2). \]

Step 3: Find relative velocity.
South components cancel: \[ 36\sqrt2-36\sqrt2=0. \] Only east component remains: \[ 36\sqrt2. \] Hence wind appears purely eastward.

Step 4: Direction of flag.
The flag points in the direction of relative wind. Hence it points towards \[ \boxed{\text{East}}. \]