# Objects A and B are at the origin. If object A moves to #(-2 ,2 )# and object B moves to #(7 ,-5 )# 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:

#### Explanation:

The components of the velocity of object A are

and object B

We're trying to find the velocity of object B with respect to object A. We'll call this velocity

The equation for relative velocity, using these frames of reference, is

And remembering that

Since we're solving for

Or, in terms of components,

Now, let's plug in our known velocity components:

Thus, the magnitude of the velocity of object B with respect to object A is

And the direction of the velocity of object B with respect to object A is

There are technically two directions that satisfy this, each opposite to each other in a coordinate plane (the other angle is thus *from* object A *to* object B, which if you were to plot their coordinates, would indeed be

The direction is more easily found in this case, as we also could have just found the inverse tangent of the differences in the