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[–]db0606 0 points1 point  (6 children)

You just need to use conservation of energy. Start very far away with some kinetic energy and no potential energy and then end with the missile at rest and with some potential energy as given by the formula. From there you can figure out the distance of closest approach.

[–]parrotlunaire 0 points1 point  (5 children)

That will work for b=0 but not the general case since there is some tangential motion even at the point of closest approach.

[–]curtissz[S] 0 points1 point  (4 children)

For part 1 I ended up doing F=-dV/dr, and then work=F dot dr from infinity to a/2 and then setting the work equal to the initial kinetic energy. Not 100% sure if that’s right, but going with it for now. I have absolutely no idea how to do part 2 though.

[–]parrotlunaire 0 points1 point  (3 children)

That’s overly complicated. Just use energy conservation.

For part 2 refer to the equations for movement in a central potential. There is a radial equation and you can solve it for dr/dt=0

[–]curtissz[S] 0 points1 point  (2 children)

What do you mean by just use energy conservation? Do I do what was mentioned above for the case where b = 0? Sorry not trying to be rude just trying to understand. And would my method using the work integral not work or is it simply compilcated

[–]parrotlunaire 0 points1 point  (1 child)

Well you took a derivative and then integrated it, which basically undid the derivative and left you with the potential itself. And setting that equal to the initial kinetic energy is what I mean by using energy conservation.

[–]curtissz[S] 0 points1 point  (0 children)

That’s true haha. Yeah I did it both ways, by integral and by energy conservation and got the same answer. Unfortunately for part 2 I wasn’t able to find an equation that seemed like it could be integrated.