# Relative Motion

## The physics lesson subject. Relative motion and relative velocity concept. Velocity with respect to observer. Finding the direction of the relative motion. Relative velocity in different locations and directions.

There is two basic element in the relative velocity concept: The observer and the observed.

The relative velocity is examines the velocity with respect to each other (Observer and observed)

A passenger in the train sees motionless objects on the roadside as if it is moving backwards. For example, an electric pole appears as going backward with speed of 60 km/h to a person travelling on a train going at 60 km/h. The speed of train that coming from opposite direction with speed of 60 km/h seems to this person as 120 km/h.

Travels persons in a train are motionless according to each other, but they are moving according to a person that sitting on the side of the road.

The relative velocity is a vector magnitude. It is has a direction and a magnitude.

The direction of the relative velocity, changes according to the location of the observer. If the moving objects are not in the same or oppsite direction, the vectors must be drawn to find the magnitude and direction of relative vectors.

**The Formula Of The Relative Velocity**

To find the relative speed, subtraction is performed between the observer vector and the observed vector.

V_{rel} = V_{A} – V_{B}

V_{rel} : is relative velocity

V_{B}: is observer

V_{A}: is observed

To find the relative velocity, the observer vector be reversed and added to the observed vector.

**Example: **

A "K" car is moving Eastwards with speed of 80 km/h. A "L" car is moving Southwards with speed of 60 km/h.

Find the velocity and direction of the "L" car with respect to the "K" car.

**Solution:**

Let we draw the velocity vector of the cars.

In this question the observer is "K" car, the observed is "L" car. We will do subtraction (L – K) operation.

The "K" vector is inverted and summed with the "L" vector.

We reverse the "K" vector and add it with the "L" vector. Thus, a right triangle is occurs. The hypotenuse of the triangle is relative velocity. It is calculated as below.

V_{rel} ^{2 } = 60^{2} + 80^{2}

V_{rel}^{2} = 10000

V_{rel} = 100

The "K" car sees the "L" car as if it going to South-west with speed of 100 km/h.

**Example:**

A bus, is moving to the North-west with speed of 80 km /h, and a car is moving to the West with speed of 120 km/h.

The angle which the bus makes with west direction is 45 degrees.

A) Find the velocity of the car with respect to the bus.

B) Find the velocity of the bus with respect to the car.

**Solution:**

Let we draw the vector of the bus and the car.

A)

When we want to find the velocity of the car according to the bus, the observer is the bus, the observed is the car.

V_{rel} = V_{car} – V_{bus}

The magnitude of resultant of two vectors that be α angle between them can be found with the formula below,

V^{2} = (V1)^{2} + (V2)^{2} + 2•V1•V2•cosα

For α = 135°

V_{rel}^{2} = 80^{2} + 120^{2} + 2.80•120•cos135°

V_{rel}^{2} = 6400 + 14400 + 1920• cos135°

V_{rel}^{2} = 34374

V_{rel} = 185.4 km/h

The car is moving to the direction of the Southwest with speed of the 184.5 km/h according to the bus.

B)

When we want to find the velocity of the bus according to the car, the observer is the car, the observed is the bus.

V_{rel} = V_{bus }– V_{car}

V_{rel}^{2} = 80^{2} + 120^{2} – 2•80•120•cos135°

V_{rel}^{2} = 6400 + 14400 – 13574

V_{rel}^{2} = 7226

V_{rel} = 85 km/sa

The bus is moving with respect to the car to the direction of the Northeast with speed of 85 km/h.

**Example:**

A person is travelling in a truck that moving the Eastward at speed of 80 km/h. At the same time, a car is moving the Westward at a speed of 90 km/h.

The person on the truck how does sees the motion of the car?

**Solution:**

In this question, the observer is the truck, the observed is the car.

Vrel = Vcar – Vtruck

Vrel = -90 – 80

Vrel = -170 km/sa

Person that on the truck is see the car as if were going toward the West with speed of 170 km/h.

**Example:**

The K and L vehicles is moving towards the West. The speed of the K vehicle is 90 km/h, and the speed of the L vehicle is 105 km/h.

A) Find the velocity of the L vehicle according to the K vehicle.

B) Find the velocity of the K vehicle according to the L vehicle.

**Solution:**

A)

In this question, the K vehicle is observer.

V_{rel} = VL – VK

V_{rel} = 105 – 90

V_{rel} = 25 km/sa

The K vehicle sees the L vehicle as if were moving the Westward with the speed of 25 km/h.

B)

In this question, the L vehicle is observer.

V_{rel }= VK – VL

V_{rel} = 90 – 105

V_{rel} = - 25 km/sa

The sign of the Vrel is negative. This mean that the direction of the Vrel is reverse. So, the K vehicle appears as if were moving toward East.

RISE KNOWLEDGE

27/07/2018

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