Relative Velocity

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Introduction

Relative velocity means its describes an object’s velocity as seen from a specific frame of reference. Analysing the movement of objects in various frames requires an understanding of relative velocity, particularly when two or more objects are moving in relation to one another. This idea is frequently applied in a variety of contexts, including examining how vehicles go on highways, boats navigate rivers, and aircraft that meet wind.
Relative Velocity-Boats Navigate Rivers
Boats Navigate Rivers

Defining Relative Velocity

Velocity is always measured in relation to a frame of reference. We can determine how quickly one thing appears to move from the viewpoint of another by comparing its relative velocity to that of the other object. Finding the difference between the individual velocities of two objects moving in the same straight line allows one to determine their relative velocity.
For example, consider two objects, A and B, moving with velocities vA and vB​ in the same direction along a straight line. The relative velocity of A with respect to B (denoted as vA / B​) is given by:
vA/B = vA − vB​
Similarly, the relative velocity of B with respect to A (denoted as vB/A)​ is:
vB/A = vB −vA​
These equations imply that relative velocity is a vector quantity and can have both magnitude and direction.
Relative Velocity-vehicles go on highways
vehicles go on highways

Cases of Relative Velocity in One Dimension

1.Objects Moving in the Same Direction

Relative velocity is the difference in the velocities of two objects moving in the same direction. For example, if A is traveling in the same direction at 10 m/s and B is going at 6 m/s, A’s relative velocity to B equals:
vA/B = 10 m/s − 6 m/s = 4 m/s
This result means that A appears to move at 4 m/s relative to B.

2. Objects Moving in Opposite Directions


Relative velocity of two objects traveling in opposite directions is equal to the total of their individual speeds. For example, the relative velocity of A with regard to B is as follows if A moves at 10 m/s in one direction and B moves at 6 m/s in the other direction:
vA/B =10 m/s + 6 m/s = 16 m/s
This result indicates that from B’s perspective, A is moving at 16 m/s.

Relative Velocity in Two Dimensions

In two-dimensional motion, relative velocity can be visualised using vector addition. Suppose two objects A and B have velocities vA and vB at different angles. The relative velocity of A with respect to B can be found by vector subtraction:
        vA/B = vA − vB​
Graphically, this can be represented by placing the vectors vA and vB​ tail-to-tail and then finding the resultant vector that represents vA/B.

Applications of Relative Velocity

1.Boat and River Problems

Solve difficulties involving boats in rivers with currents, relative velocity is essential. When a boat attempts to cross a river, its speed in relation to the bank is determined by the river’s current as well as its speed in still water. The boat’s effective velocity and the angle it should head to reach a destination can be found by computing the relative velocity.

2. Airplane and Wind Problems

When airplanes encounter wind, they experience relative velocity problems, much like boats in a river. Vector sum of the two velocities can be used to calculate the airplane’s velocity with respect to the ground if its velocity with respect to the air is known and its velocity with respect to the wind is also known.

3. Cars on a Road

Knowing relative velocity on a roadway can assist drivers judge whether they are getting closer to or farther away from other cars. For example, if two automobiles are traveling in the same direction, the driver of one car can determine how rapidly they are passing the other by comparing their speeds.

Importance of Frame of Reference

Relative velocity idea emphasises how vital it is to select the right frame of reference. A frame of reference is the perspective that an observer uses to quantify and characterise motion. An object’s relative velocity may seem differently depending on the frame that is selected.
Relative velocity of two individuals approaching one another from a fixed location is just the sum of their individual speeds. But if we look at it from one person’s perspective, the other person seems to be coming much more quickly.

Note

A fundamental idea in both one-dimensional and two-dimensional motion analysis is relative velocity. It offers important information on how things seem to move in relation to one another when viewed from various frames of reference.
We may more effectively examine how items move in real-world situations, such as cars on roads, boats in rivers, and airplanes in windy circumstances, by computing relative velocities. This knowledge not only makes difficult motion problems easier to understand, but it also provides a basis for more complicated mechanical concepts.
Velocity of an object as apparent from a specific frame of reference that is moving in relation to the object is known as its relative velocity. From the viewpoint of another moving object, it indicates how quickly and which way an object appears to be traveling.
When two items travel in the same direction along a straight line, the difference between their individual velocities is used to determine the relative velocity of one object with regard to the other:
vA/B = vA − vB​
where vA and vB​ are the velocities of objects A and B, respectively.
The relative velocity of two objects moving in opposite directions is determined by summing their individual velocities. For instance, if A and B have velocities vA and vB and are traveling in opposite directions, then A’s relative velocity to B is:
vA/B = vA + vB​
Two moving things appear to interact from one another’s points of view requires a grasp of relative velocity. Applications for it include figuring out how fast cars are traveling in relation to one another on roadways, figuring out how fast boats are going in flowing rivers, and taking wind into consideration when airplanes flying.
In two-dimensional motion, relative velocity is calculated using vector subtraction. For example, if two objects A and B have velocities vA and vB in different directions, the relative velocity of A with respect to B is:
vA/B = vA−vB​
This involves both magnitude and direction, and is often represented graphically using vector diagrams.
Because an object’s relative velocity can change based on the observer’s point of view, a frame of reference is essential. Selecting a frame of reference makes motion analysis easier. Two persons approaching one another may have a combined relative velocity if you are looking at them from a fixed position, but if you are looking at it from one person’s perspective, the other person appears to be approaching more quickly.
Yes, if two objects are traveling in the same direction and at the same speed, their relative velocities can be zero. Because their distance from one another hasn’t changed throughout time, they appear to be stationary from each other’s point of view.

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