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On a day when the wind is blowing toward the north at 6 m/s, a runner jogs west at 5 m/s. What is the velocity (speed and direction) of the air relative to the runner?

Answer :

Final answer:

The velocity of the air relative to the runner is approximately 7.81 m/s in a direction 22.1° south of west.

Explanation:

To find the velocity of the air relative to the runner, we need to calculate the vector sum of the runner's velocity and the wind velocity. Since the wind is blowing towards the north at 6 m/s, we can represent it as a vector with magnitude 6 m/s pointing upwards. The runner is jogging west at 5 m/s, which can be represented as a vector with magnitude 5 m/s pointing to the left. By adding these vectors, we can find the resultant velocity. We may get the size of the resultant velocity using the Pythagorean theorem:

Magnitude: √((6 m/s)² + (5 m/s)²) ≈ √(36 + 25) = √61 m/s ≈ 7.81 m/s



The direction of the resultant velocity can be found by calculating the angle it makes with the west direction. Trigonometry can be used to determine the angle:

Angle: tan⁻¹((6 m/s)/(5 m/s)) ≈ tan⁻¹(1.2) ≈ 22.1°


So, the velocity of the air relative to the runner is approximately 7.81 m/s in a direction 22.1° south of west.

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