IMPACT OF TWO MOVING BODIES 247 



As before, let the velocities along AB before impact be u, u f , I 

 these both being measured in the direction AB, and let the | 

 velocities in the same direction after impact be v, v'. Then we 

 have, by the conservation of momentum along AB, 



mu + m'u r = mv + m f v f , 

 and, by Newton's law, v v' = e (u u'}. 



From these equations (88) and (89) follow as before. 



FIG. 128 



If the velocities of A before impact make angles a, a' with AB 

 as marked in the figure, the tangential velocities of A before and 

 after impact are 



so that, since the tangential velocities remain unaltered, we 

 must have ^ tana'= - tana; 



while similarly, from the motion of B, 



Thus equations (88) and (89) become 



. mu + m'yJ em'(u u') 



cot a' = -- * - - cot a, 



(m + m)u 



cot/3'= - *"* + ''+ (-' 



(m -\- m!}u' 



giving a', @ f in terms of the initial motion. 



