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You are holding a flag. When you run at 8 m/s due east, the flag flutters to the north. When you run at 2 m/s due south, the flag flutters to the northeast. If the wind velocity is uniform and remains constant, find the wind velocity.

Answer :

Final answer:

Determining the wind velocity involves constructing an accurate vector diagram based on the motion of the flag as compared to the person's motion. Applying Pythagorean theorem and trigonometric functions, the magnitude and direction of the wind velocity can be found.

Explanation:

For systematic calculation of wind velocity, vectors must be used appropriately. Initially, when the person is moving due east at 8 m/s and the flag is fluttering towards north, the wind velocity vector must be towards north as it is perpendicular to the direction of the person's motion.

During the second instance, when the person is moving towards south at 2 m/s and the flag flutters in the northeast, the wind velocity vector again must be in the northeastward direction. Using these information, we can construct an equation and a vector diagram to find the magnitude and direction of the wind velocity.

To do this, we know the sum of the two vectors (person's velocity vector and the wind velocity vector) gives the resultant direction of the flag flutter. Using Pythagorean theorem and trigonometric functions, we could calculate the magnitude and angle of the wind velocity.

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