Collision of elastic Bodies. 189 



for the velocity of the impinging body after collision 1 |, and, for 

 that of the impinged 5 |. 



If the impinged body, instead of 7 ounces, had a mass of 20 

 ounces ; the velocity, after collision, the bodies being considered 

 as unelastic, would be, 



If from double this quantity or 5 f , we subtract the velocities be- 

 fore collision, namely, 6 and 2 respectively, we shall have, 



5 I _ 6 an( j 5 | 2, 

 that is 



I and 3 



for the velocities after collision, in which the sign before f 

 indicates that the impinging body would rebound. 



If the two bodies are made to move in opposite directions 

 with the same masses and the same velocities, as in the first of 

 the above examples, the velocity after collision, the bodies being 

 considered as unelastic, would be 



5x6 7x2 30 14 



12 



lj& __ 





If from double this velocity or 2 f , we subtract the velocity 6, 

 which the impinging body had before collision, we shall have 

 3 i for its velocity after collision ; it will rebound, therefore, 

 with a velocity of 3 \ feet. As to the impinged body, it will be 

 recollected that to twice 1 \ or 2 f , the velocity before collision 

 is to be added, which gives 4 f for its velocity after collision. 297. 



301. Since, when elastic bodies move in the same direction 

 before collision, the velocities after collision are 297. 



2 u' u and 2 u' i>, 



u f being the velocity which they would have, considered as une- 

 lastic ; the difference u v of these two velocities, is the same 

 as the difference of the velocities before collision. This difference 

 is called the relative velocity, and is accordingly the same be- 

 fore and after collision. 



