39, 40] RELATIVE MOTION. 41 



Join HK. Then the vector OK is compounded of OH, HK. 



Hence HK represents the displacement of B relative to A in 

 magnitude, direction, and sense. 



Now the vector HK is the resultant of HO, OK. 



Hence to obtain the displacement of B relative to A we must 

 compound the displacement of B with the reversed displacement 

 of A. The resultant is the required relative displacement. 



In the same way the \ , / \ of B relative to A is the 

 [acceleration] 



j ve oci y ) ^- k mus t be compounded with the \ , . I 

 (acceleration} [acceleration] 



of A in order that the resultant may be the ! . . j- of B. 



Since the velocity of a point in any direction is the rate of 

 increase of its displacement in that direction per unit time, and 

 since its acceleration in any direction is the rate of increase of its 

 velocity in that direction per unit time, we have the rules : 



The I ve } oclt y I of B relative to A is the resultant of the 

 [acceleration] 



of B and the of A reversed. 



[acceleration] [acceleration] 



The compositions and resolutions described in this Article are 

 to be effected as if the vectors involved were not localised, but 

 the velocity and acceleration of B relative to A are to be regarded 

 as localised in lines through B. 



