Chapter 1: Problem 6

A wind is blowing from the north (the air is moving toward the south). When a person is walking toward the north, is the relative speed of the wind that the person senses greater than, the same as, or less than the speed the person senses when not walking? How about when the person is walking toward the south?

Short Answer

Expert verified

Explain. Answer: A person experiences a greater relative speed of wind blowing from the north when walking towards the north. This is because their walking speed is against the direction of the wind, resulting in a sum of the absolute speeds, which will be greater than the wind speed alone when the person is not walking. Conversely, when walking towards the south, the person's walking speed adds to the speed of the wind, creating a smaller relative speed than when not walking.

Step by step solution

Understanding the Problem

In this exercise, we have a wind blowing from the north (i.e., towards the south), and a person walking either towards the north or towards the south. We need to determine the relative speed of the wind that the person experiences in these situations.

Notations

Let's denote the following speeds: - \( v_w \): speed of the wind blowing towards the south (given) - \( v_n \): speed of the person walking towards the north - \( v_s \): speed of the person walking towards the south Note that the person cannot walk at the same time towards the north and the south, but we set up the notations for both situations.

Calculating Relative Speed

To find the relative speed of the wind that the person senses, we need to consider the difference in velocities between the person and the wind. When the person is walking towards the north, their speed will be against the direction of the wind, so we sum the absolute speeds: \( v_{rw_n} = v_n + v_w \) When the person is walking towards the south, their speed adds to the speed of the wind, so we subtract the absolute speeds: \( v_{rw_s} = v_w - v_s \) Now let's consider the person senses when not walking.

Relative Speed When Not Walking

When the person is not walking, their speed is 0, so the relative speed they experience is just the speed of the wind moving towards the south: \( v_{rw_0} = v_w \)

Comparing Relative Speeds

Now we can compare the relative speeds of the wind that the person senses. 1. When the person is walking towards the north: \( v_{rw_n} = v_n + v_w \) which is greater than \( v_{rw_0} = v_w \), since the person's walking speed is non-negative. 2. When the person is walking towards the south: \( v_{rw_s} = v_w - v_s \) which is less than \( v_{rw_0} = v_w \), since the person's walking speed is non-negative. So, the relative speed of the wind the person senses is greater when they are walking towards the north than when they are not walking and less when they are walking towards the south than when they are not walking.

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Short Answer

Step by step solution

Understanding the Problem

Notations

Calculating Relative Speed

Relative Speed When Not Walking

Comparing Relative Speeds

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