Can someone help me with the followingproblem? I tried setting up the two equati

Question

Can someone help me with the followingproblem? I tried setting up the two equations and I am pretty sureI did it correctly, but for some reason I can't get the rightanswer.

Ball A has mass 5.0 kg and is moving at 3.2 m/swhen it strikes stationary ball B, which has mass 3.9 kg, in ahead-on collision. If the collision is elastic, what is thevelocity of (a) ball A, and (b) ball B after the collision?

This is my work:

mavai + mbvbi =mavaf +mbvbf
(5*-3.2) + (3.9*0) = 5vaf+ 3.9vbf

I solved that for vaf and gotvaf= -3.2-0.78vbf


Then I used the formula for total kinetic energy:

(1/2)mav2ai +(1/2)mbv2bi =(1/2)mav2af +(1/2)mbv2bf

After plugging in numbers and substituting equations, Igot this:
-6.942v2bf-24.96vbf = 0

However, when I graph the equation I get zero which is said to beincorrect. Can anyone please explain where I went wrong and ifthere is a simpler way to do this? Thanks in advance.

Explanation / Answer

Consider the ball B at rest at initially    the final velocity    v1f = (m1 - m2 ) / (m1 +m2) v1i    = [(5-3.9) /(5+3.9)](3.2) = 0.395 m/s the final velocity    v2f =[ 2m1 / (m1 + m2)] v1i    =[ (2 *5 ) / (5+3.9)](3.2)    = 3.59 m/s          = [(5-3.9) /(5+3.9)](3.2) = 0.395 m/s the final velocity    v2f =[ 2m1 / (m1 + m2)] v1i    =[ (2 *5 ) / (5+3.9)](3.2)    = 3.59 m/s          =[ (2 *5 ) / (5+3.9)](3.2)    = 3.59 m/s      

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