# Objects A and B are at the origin. If object A moves to #(-3 ,1 )# and object B moves to #(-6 ,3 )# over #3 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

##### 1 Answer

#### Answer:

From **A**'s perspective **B** would increase the distance from **A** with a speed

#### Explanation:

We have to assume that **A** and **B** objects move with constant speeds, each in its own direction, from the perspective of an observer positioned at the origin of coordinates.

So, every second each object covers the same distance.

Assume, object **A**'s positions at seconds **B** at these moments are

Obviously, all points

Also, since the speed of each object is constant,

A simple theorem of geometry tells that triangles

That means that vector expressing the relative velocity of object **B** from the perspective of object **A** has always the same direction and magnitude.

Let **A**, its X- and Y-components are

Analogously, **B** with components

If **i** and **j** are unit vectors along, correspondingly, the X-axis and the Y-axis, object **A**'s position as a function of time

**i** **j** .

Analogously, object **B**'s position is described by as

**i** **j** .

Relative position of object **B** from the perspective of object **A** (that is if we imagine object **A** to be an origin of a system of coordinates moving with it) is expressed as a difference between the two vectors above, that is

**i** **j****i** **j**

**i** **j**

The above implies that object **B** moves relatively to object **A** with constant speed towards the same direction. Relative velocity is a vector

Obviously, in meters per second (

The relative movement of object **B** is described by a vector of velocity

Knowing the components of this vector of relative velocity of object **B** from the perspective of object **A**, we can easily determine the magnitude:

So, from **A**'s perspective **B** would increase the distance from **A** with a speed