Coefficient of Restitution? PLEASE HELP!!!

arpitm08

1. The problem statement, all variables and given/known data

Two balls of equal mass moving with the speed of 3 m/s, collide head on. Find the speed of each after impact if the coefficient of restitution is 1/3.

2. Relevant equations

e=(v2-v1)/(u1-u2)
v2= velocity after impact of object 2
v1= velocity after impact of object 1
u2= velocity before impact of object 2
u1= velocity before impact of object 1

3. The attempt at a solution

I put the numbers into the equation and it yield 0 over something.
The answer is 1 m/s for both ball, but with that into the equation, it would yield 0/0.
My book doesn't say anything on how to do this problem. Maybe it is as simple as multiplying the velocities by 1/3 to get the answer.
Could someone please help me out?

Doc Al

Since the balls approach each other, one has a velocity of +3 m/s while the other has a velocity of -3 m/s.

arpitm08

yes that is true, but i just copied the problem exactly from the book.

Doc Al

There's nothing wrong with the problem statement, just with your attempted solution.
That just means you input the wrong numbers. Realize that u and v are velocities, not just speeds.

ajinx999

Considering
u1 = 3 m/s
u2 = -3 m/s
e = 1/3
e = (v2-v1)/(u1-u2)
→ v2-v1 = 2 m/s
u1+u2=v1+v2
...(conservation of linear momentum)
→ v1+v2 = 0
→ v1 = -v2
Therefore, the speed of each ball after impact is 1 m/s.