Relative Velocity 

The calculations in the examples
on the page Relative Speed were very simple (I was going to say relatively simple... but decided against it...) because we
only considered bodies moving along the same straight line. 



To find the velocity of one body relative
to another when they move in different directions (that is,
not along the same straight line) we use the same
principle but the
subtraction will have to be a vector subtraction, which, you will
recall, is just a vector addition with one of the arrows inverted. 

For example, consider two cars moving as
described below. 

Car A moves at 20ms^{1}
towards the east. 

We will write this velocity as v_{A(O)}
as in the relative speed examples (but here using bold print to remind us that
we are considering the vector nature of velocity). 



Car B moves at 15ms^{1}
towards the north. 

This is velocity v_{B(O)}.
In each case, "O" is simply some fixed point on the earth relative to which
these velocities have been measured. 



To find the velocity of car A relative to car B we must perform a vector subtraction







Arrow representing
v_{A(O)} drawn to scale. 



Arrow representing
v_{B(O)} drawn to scale then inverted to give v_{B(O)} 






Triangle of vectors to perform the addition, 







From this we find that the velocity of A relative to B, v_{A(B)}
has magnitude 25ms^{1} in
a direction θ = 39.6° south of east. 



As was stated on the Relative Speed page, in case this all seems pretty obvious and
intuitive, be warned...
when Einstein looked at this more closely, he found it to need
significant modification when
the relative speeds involved are very great (see the
Relativity sections). 
