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Relative Speed and Velocity (3)
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 vA(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 vB(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 vA(O) drawn to scale.  
Arrow representing vB(O) drawn to scale then inverted to give -vB(O)  
   
   
Triangle of vectors to perform the addition,  
 
   
   
From this we find that the velocity of A relative to B, vA(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).  
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