COL 



hard bodies, a and b their velocities before impact, r the common velo- 

 city after impact, then 



A a + B b 



4. or , according as they move in the .same or opposite directions be- 

 fore impact. 



<t -j- b 

 Cor. 1. When the bodies are equal, v -~ = . 



Cor. 2. When B is at rest or b = o, v 



2. In the direct impact of two perfectly hard bodies A and B, if g 

 velocity gained by B, and I velocity lost by A after impact ; 



or -|-, according as they move in the same or opposite directions. 



Cor. g _j_ / a ^ b. 



II. Of (Tie impact of perfectly elastic bodies. 



1. Let r = relative velocity of two bodies = a T J, according as they 

 move in the same or opposite directions, g velocity gained by B in the 

 direction of A's motion, / = velocity lost by A in that direction - t then in 

 the direct impact of two perfectly elastic bodies, 



*==-*A- 



- A-J-B' 



A + B' 



Cor. 1. If A B, B's velocity after impact = a, and A's velocity 

 i b, i. e. the bodies interchange velocities. 



Cor. 2. In the congress of perfectly elastic bodies, the relative velocity 

 after impact the relative velocity before. 



Cor. 3. If a' and b 1 be the velocities after impact, 

 A 2 -f B b 9 = A a' 8 -f B b'*. 



Cor. 1, If there be a row of elastic bodies A, B, C, D, &c. at rest, and 

 a motion communicated to A, and thence to B, C, D, &r. ; then, if the 

 bodies arc equal, they will all remain at rest after impact, except the last, 



