A proton and an “positron” (identical to an electron, except positivel

1. The problem statement, all variables and given/known data
A proton and an "positron" (identical to an electron, except positively charged) are brought 6 µm apart and released from rest.

a.) What is the initial potential energy stored by this system? 3.84e-23 J

b.) In this problem, we’ll let BOTH charges move. The collective kinetic energy of the charges (Ksys) will be drawn from Usys. However, since both charges are moving, they will need to "share" this energy.

Once in motion, what percentage of Ksys does each charge have at any given moment?
proton: K = . % of Ksys
positron: K = . % of Ksys
(In this scenario, how valid is our usual approximation to assign the entire Usys to one particle? Which particle should it be assigned to?)

What is the speed of each charge after they have repelled a long distance apart?
proton: vf = . m/s
positron: vf = m/s

2. Relevant equations

electric potential = kqq/r
energy conservation equations =
KEi+PEi=KEf+PEf
((1/2)mvi^2)+(kqq/r-initial)=((1/2)mvf^2)+(kqq/r-final)

momentum conservation
M1V1=m2v2

proton: mass (1.67E-27kg) positron: mass (9.11E-31kg)

3. The attempt at a solution

for part a)
electric potential = kqq/r
((9E9)(1.67E-27)(1.67E-27))/(6E-6) = 3.84E-23

i have problem on part b where i have to find the speed of positron and proton, also the percentage of KE of proton and positron have after being released and both moving away from each other

i set up the equations using energy conservation method to solve the velocity first because i thought if i can find the velocity then i know the KE ratio of proton and positron have

the formula to find the velocity is in the picture.
that is how i set it up but after i find the velocity and use it to find another velocity i got it wrong. can someone help me with this? i really appreciate it if you can show me the right way to solve for each velocity of proton and positron.
thank you so much

Attached Images
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