3 balls in a moving mechanics problem

[Manolisjam]

I do not consider the time I gave freely to you wasted. If you are willing to pick up at post #26 and reconsider your expressions for the initial and final potential energy, please do so and I will continue guiding you. If not, not.

Solved it!

 

[haruspex]

Solved it!

This is a duplicate of
https://www.physicsforums.com/threads/classical-mechanics-problem-with-balls.940763/
@Manolisjam , please do not duplicate threads to garner a wider audience. If you wish to bring others in you can either use the "@" link to bring in specific people, or ask your current respondent (me, in this case) to do it. Or even "report" the thread to the mentors.

Anyway, you claim to have solved it, and I think that may be true for the collision velocity if you figured out how to write the energy equation correctly, but I do not see how you will have found the time that way.
Have you found time to collision?

 

[Manolisjam]

This is a duplicate of
https://www.physicsforums.com/threads/classical-mechanics-problem-with-balls.940763/
@Manolisjam , please do not duplicate threads to garner a wider audience. If you wish to bring others in you can either use the "@" link to bring in specific people, or ask your current respondent (me, in this case) to do it. Or even "report" the thread to the mentors.

Anyway, you claim to have solved it, and I think that may be true for the collision velocity if you figured out how to write the energy equation correctly, but I do not see how you will have found the time that way.
Have you found time to collision?

At the 0 point using conservation energy i get something like u_a^2+u_g^2=2gsinθl now i know dx/dt=u_a=lsinθdθ/dt . find same way u_G now squaring those. andi plugging them in conservation i get Ldθ/dt=sqrt(2sinθ) this is a differential eq separable. find θ(t) and solve for θ=π/2 but i can't solve the integral

 

[Manolisjam]

At the 0 point using conservation energy i get something like u_a^2+u_g^2=2gsinθl now i know dx/dt=u_a=lsinθdθ/dt . find same way u_G now squaring those. andi plugging them in conservation i get Ldθ/dt=sqrt(2sinθ) this is a differential eq separable. find θ(t) and solve for θ=π/2 but i can't solve the integral

if you can show me another way for the time. i still haven't understant what you are trying to help me do.

 

[haruspex]

if you can show me another way for the time. i still haven't understant what you are trying to help me do.

Ok, you have found another route to the same equation. (Your final equation is not quite right: check the powers of L and g in it.)
In case it helps in future, if two objects remain a constant distance apart then they must have the same velocities and accelerations along the line joining them. Hence a_Acos(θ)=a_Gsin(θ).
I'll get back to you on solving the integral.

 

[haruspex]

I'll get back to you on solving the integral

It seems to involve elliptic integrals. Nasty.
http://www.wolframalpha.com/input/?i=integrate+(sin(x))^(-1/2)dx+from+x=0+to+pi/2

 

[kuruman]

It seems to involve elliptic integrals. Nasty.

Yes, it is nasty. It's a bit simpler if all masses start from rest and along the horizontal line through the origin, but still an elliptic integral. Considering that OP is a math undergrad, this is perhaps a math exercise that assumes understanding of physics to get to the math. I would be curious to see what the solution is according to the person who assigned the problem.