What are the final velocities of two balls after an elastic head-on collision?

[Arooj]

Homework Statement

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?

Homework Equations

http://www.nvcc.edu/home/tstantcheva/231files/G09_hw.pdf
 
I used the derived equation from page 4.

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.

 

[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.

 

[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?

 

[frogjg2003]

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

 

[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.

 

[frogjg2003]

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