What exactly is the physics behind the shepherd moons?
Take Pandora and Prometheus of Saturn for example, they keep the F-ring in line by their combined gravitational effects, I went though a lot of books but all of them are quite general hand-waving kind of explanation and nothing...
for head to tail rule, imagine you have 2 match sticks,
arrange the match stick in such a way that the head of the stick (call it S1) is touching the tail of the other one (S2).
Now draw a stright line from the tail of S1 to the head of S2, that would be your new vector, S1 + S2.
for...
in a frictionless enviroment, all kinetic energy should be converted into potential energy. so the difference between max. kinetic and max potential energy is what you should be looking for.
Hmmm, big no on that.
You split the velocity into x-y components which is good, but your choice of formula for part 1 is somewhat questionable. See the question have not given you how long the bullet stays in the air, and therefore you would have 2 unknowns in d=ut + 1/2 at^2. it's still...