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For question 3) c) iii) Is the Earth part of the system? Based on the answer given, it is but the question refers to "the clay-ball system's path".

Katherine, thank you very much; you are correct. I fixed the problem set. John

I am confused on the answer for question 6. The velocity graphs in Parts b and  c would not result in momentum being conserved.  If the small ball bounces back and has negative momentum after the collision, would not the large ball need to have some positive velocity to make the total final momentum positive?  Or are we assuming that the system is just the small ball?  Also, on Part d, would not the change in momentum need to be equal?  If both balls experience the same force for the same amount of time, the impulse would be the same, and therefore the change in momentum would also be the same would not it?

Cristine, you are correct if we didn't make some simplifying assumptions. Combining the conservation of KE and conservation of momentum, we come up with a more complex equation. The assumptions let us say that the large object doesn't move at all, so the small object bounces off with the same energy. 

Please refer to the presentation, starting on slide 121 to see the equations and the approximations.
I will add to the question that we are assuming an ideal world for this to work.

John

https://njctl.org/materials/resources/momentum-presentation-3/attachments/