Understanding Relative Velocity: Calculations and Examples

Relative velocity is a fundamental concept in physics that is often used to understand the motion of one object relative to another. This article will explore the concept of relative velocity, provide a step-by-step guide to solving relative velocity problems, and present examples to illustrate the calculations.

What is Relative Velocity?

Relative velocity is the velocity of an object as observed from a reference frame of another object. It is the difference between the velocities of two objects.

Example Problem: Calculating Relative Velocity

Consider two cars, car A and car B, moving on a straight road in the same direction. Car A is moving at 60 km/h, and car B is moving in the same direction at 10 m/s. The goal is to understand the relative velocity of each car with respect to the other.

Step 1: Convert Units Consistently

In the given problem, car A's velocity is already in km/h. Car B's velocity is given in m/s, which needs to be converted to km/h.

[ vec{v}_B 10 , text{m/s} times left( frac{1000 , text{m}}{1 , text{km}} right) times left( frac{1 , text{h}}{3600 , text{s}} right) 36 , text{km/h} ]

Step 2: Finding the Relative Velocity of Car A with Respect to Car B

The relative velocity of car A with respect to car B (denoted as (vec{v}_{A text{ wrt } B})) is:

[ vec{v}_{A text{ wrt } B} vec{v}_A - vec{v}_B ] [ 60 , text{km/h} - 36 , text{km/h} 24 , text{km/h} ]

So, car A is moving 24 km/h faster than car B.

Step 3: Finding the Relative Velocity of Car B with Respect to Car A

The relative velocity of car B with respect to car A (denoted as (vec{v}_{B text{ wrt } A})) is:

[ vec{v}_{B text{ wrt } A} vec{v}_B - vec{v}_A ] [ 36 , text{km/h} - 60 , text{km/h} -24 , text{km/h} ]

This negative value indicates that car B is moving 24 km/h slower than car A.

Additional Examples

Let's consider another scenario where car A travels at 70 km/h, and car B travels at 50 km/h in the same direction:

Step 1: Velocity of Car A Relative to the Fixed Point

If the reference frame is fixed, an observer will see car A traveling at 70 km/h, and car B traveling at 50 km/h, both in the same direction.

Step 2: Velocity of Car B Relative to Car A

[ vec{v}_{B text{ wrt } A} vec{v}_B - vec{v}_A ] [ 50 , text{km/h} - 70 , text{km/h} -20 , text{km/h} ]

This means car B appears to be moving 20 km/h slower than car A.

Step 3: Velocity of Car A Relative to Car B

[ vec{v}_{A text{ wrt } B} vec{v}_A - vec{v}_B ] [ 70 , text{km/h} - 50 , text{km/h} 20 , text{km/h} ]

This means car A appears to be moving 20 km/h faster than car B.

These examples demonstrate how relative velocity can be calculated and how it can be used to understand the motion of objects in different reference frames.

Conclusion

Understanding relative velocity is crucial in many fields, including physics, engineering, and transportation. By converting units and properly calculating the difference between velocities, you can accurately determine the relative motion of objects. For more complex scenarios, it's always a good idea to consult a physics teacher or reference materials.