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In physics, the relative velocity is the velocity of an object in a given direction as measured by an observer whose position is moving at a constant velocity relative to the object.
The formula for relative velocity is:
VAC=VAB+ VBC
Where,
VAB = Velocity of object A with respect to object B
VBC= Velocity of object B with respect to object C
VAC = Velocity of object A with respect to object C.
This blog will go through a basic introduction of relative velocity, Dimension of relative velocity, and some sample problems related to this concept.
Relative Velocity
In some cases, an object may move in a medium that is moving. For example, a boat could be sailing on the surface of water that is flowing at some rate. When we assess these kinds of motions, we have to consider how the movement the object makes compares to the medium’s motion and each object’s relative velocities. We can figure out their combined velocity by adding together the speeds of both the object and medium and subtracting the relative velocity between them.Relative Motion in One Dimension
In the context of kinematics, we speak of relative motion if at least two reference frames are involved in a phenomenon. There is a one-dimensional example that serves as a building block to understanding how to treat relative motion for different speeds and directions in more than just one dimension. Vector components can be decomposed and then combined using their parts to calculate the relative velocity using this rule. An example, a person sitting on a train moving at 10m/s towards the east. Assume that the east direction is chosen as the positive direction and the earth is chosen as the reference frame.. The velocity of the train with respect to the ground frame would be, VTE = 10 m/s Now let’s say the person on the train gets up and starts walking in an opposite direction to that of the train. He is moving at 2 meters per second inside the train. This velocity is with respect to a reference situated within the train itself.The velocity of the person is, VPT = -2 m/s These two vectors can be added to find the velocity of that person with respect to the earth. The sum is called relative velocity. vPE = VTE + VPT vPE = 10 m/s + (-2 m/s) vPE = 8 m/sRelative Motion in Two Dimensions
Let’s consider two objects, say object A and object B, that are moving at the respective velocities Va and Vb relative to some common reference frame. For example, these could be the velocities of objects A and B with respect to the ground. In this case, the velocity of object B relative to object A could be – A relative to that of B would be – Vab= Va – Vb Similarly, the velocity of object B relative to A would be : Vba = Vb– Va Therefore, Vba= – Vba | Vab | = | Vba | When two objects seem to be stationary, in that case – Vb = Va Vba = Vab = 0 When the magnitudes of Va and Vb are the same sign, object A will move slower than object B because the magnitude of their relative velocity is less. When Va and Vab have the same sign, object A may appear to be moving faster when it’s actually not moving at all, because the magnitude of its velocity relative to itself or B isn’t necessarily as great as that of Vb in relation to itself or A. Similar reasoning may apply when objects A and B are in opposite directions.Sample Problems
- A train moves at a speed of 100 km/h. A person inside the train starts moving at 10 km/h in the opposite direction of the train. Find the relative speed of the person with respect to the train.
- A vehicle is moving at a speed of 3i + 4j m/s. The person inside the car thinks the bird is flying at a velocity of 2i + 2j m/s. Find the speed of the bird with respect to the car.
- Alice is walking in the direction of a train that’s traveling at 100 km/h. Due to the motion of the train, Alice is traveling 25 km/h relative to the ground. What is the velocity of Alice with respect to the train?
