Chapter 28.8, Problem 1EE

Please answer the first three questions. PLEASE DO NOT SKIP ANY STEPS AND COMPLETELY EXPLAIN YOUR ANSWER. I have submitted this question now three times and have gotten different answers each time. Please make sure to answer the first question in terms of AU!! Please double check your work, and please make sure you fully undrestand the question before you undertake the problem.

Please help me with this problem and needed correct answer.. I can't even comment here so please don't send wrong Answers.. Wrong answers will simply unliked

The law of conservation of energy states that energy can be converted from one form to another but cannot be created or destroyed. Therefore, the amount of energy in the universe is constant. In your initial post to the discussion, respond to the following prompts: What do you think would happen if energy were not conserved? Think of (and share) two scenarios in which our lives would be drastically altered if this law of conservation was not in place. At least one of your scenarios should be at the molecular level. Would the implications be positive? Negative? Explain.

Please explain how you got the answer for this, thank you so much!

Hi.  I still don't get it.  I'm not sure what sin and cos have to do with it.  But either way, I'm still stuck in the same place.   I don't know how you got from steps 3 and 4 to the next step.  One is for the x-axis and the other for the y-axis.  How did they end up merged together?  If you apply the Pythagorean theorem, you get either:v = sqrt{(vcos) 2 + (vsin) 2}  Then what?  Or you get:v = sqrt{(m1v1/m1+m2)2 + (m2v2/m1+m2)2}   Now what?  That "adding" step just looks like the Pythagorean theorem, with v2 being the c in c2 = a2 + b2, but what is going on on the other side of the equation?   I don't understand how in the denominator you went from:(m1 + m2)2 + (m1 + m2)2 to(m1 + m2)2It seems to me like (m1 + m2)2 + (m1 + m2)2 = 2(m1 + m2)2 Explain as if I didn't understand the algebra, because I think that's the issue here.

See the screenshot uploaded. Answer in a step-by-step format, add diagrams, and detailed side notes for a better understanding. For a more clear response please answer on paper  Thank you!

I'd like an answer to part "C" only and explanation if possible so I know how deal with these kind of problems in the future.

MAKE AN FBD FOR THIS ONE. PLEASE DO IT COMPLETELY. THANK YOU. I REPEAT ONLY FBD NO NEED FOR ANSWERS.

Please solve this entire question for me. Thank you.