A north wind is blowing (the air is moving towards the south). When a person is walking towards 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 towards the south?

In physics, the concept of a frame of reference is indispensable when describing the motion of objects. It's essentially a point of view from which the observer measures and witnesses events. For example, if you're standing on the side of a road, your frame of reference is the ground you're standing on. However, if you're in a moving car, your frame of reference changes to the car.

Imagine observing an airplane flying overhead while you stand still versus while you're running. The airplane's motion appears different due to your changed frame of reference. In our exercise, the person walking north or south provides their frame of reference. When not walking, the earth can be considered the frame of reference. Understanding that we can view the same event differently depending on our frame of reference is crucial to grasp how relative velocity works.

Velocity is more than just speed; it's speed with direction. Think of it as the fast-forwardness of an object in a particular direction. Measured in meters per second (m/s) or kilometers per hour (km/h), it tells us how quickly something is displacing from one point to another. In the context of our exercise, the velocity of the wind (denoted as \(V_{wind}\)) and the velocity of the person (denoted as \(V_{person}\)) are key ingredients to compute the relative velocity.

Components of Velocity

In a two-dimensional space, like the surface of Earth, velocity can be broken down into horizontal and vertical components. However, in our scenario, only the horizontal component matters – the wind's speed along the north-south axis, and likewise for the person's walking speed.

When we say relative speed, we're looking at how fast one object is moving with respect to another. Unlike absolute speed, which is the speed of an object relative to a stationary background, relative speed depends on the observer’s motion. It’s often experienced in daily life, like when you're on a train watching another train pass by—each train's speed seems different depending on your point of view.

In the exercise, when the person walks north, the relative speed of the wind feels greater because the person’s movement counters the wind’s velocity, essentially adding to the wind’s speed from the person’s perspective. Conversely, walking south lowers the relative wind speed from the person’s viewpoint since both are moving in the same direction. Here, the formula \(V_{relative} = V_{wind} - V_{observer}\) is utilized to calculate the sensed wind speed, accounting for the directions of both the wind and the person walking.