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.
From A's perspective B would increase the distance from A with a speed
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
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.
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
Analogously, object B's position is described by as
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
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