1. Oct 27, 2012

### Arooj

1. The problem statement, all variables and given/known data
A 2.0 kg ball is traveling east at 8.0 m/s when it has a perfectly elastic head-on collision with a 3.0 kg ball traveling west at 10.0 m/s. What are the final velocities of the two balls?

2. Relevant equations

http://www.nvcc.edu/home/tstantcheva/231files/G09_hw.pdf [Broken]

I used the derived equation from page 4.

3. The attempt at a solution
For the 2.0 kg ball I got -13.6 m/s.
For the 3.0 kg ball I got -15.6 m/s.

Last edited by a moderator: May 6, 2017
2. Oct 27, 2012

### frogjg2003

Please show your work. The new speeds for both balls are faster than either initial speed. Elastic collisions conserve energy. Your speeds indicate energy was somehow created.

3. Oct 27, 2012

### Arooj

vf1 = ((m1)(v1) + m2((2*v2) - v1)) / m1 + m2
vf1 = (16 + 3(-20 - 8))/5
vf1 = -13.6 m/s

vf2 = v1 + vf1 - v2
vf2 = 8 + -13.6 - 10
vf2= -15.6 m/s

I'm assuming my problem is from setting the values of the speeds in the opposite direction to negative, but I thought this must be done?

4. Oct 27, 2012

### frogjg2003

You have a sign error for the second velocity. What is -v2?

5. Oct 27, 2012

### Arooj

Ah I see what I did wrong, v2 = 4.4 , and v1 = -13.6, substituting them into the conservation of momentum equation yields 14 = 14.

6. Oct 27, 2012

### frogjg2003

You are right. Since you're checking momentum, you should also check energy as well. There are two conservation theorems to satisfy.