How do you move a part at a certain angle?[Solved] [closed]

I was writing a complete answer when I got stuck.

My conclusion: You can't do this. Why? It requires excessive math and even equation solvers like Wolfram Alpha can't do it. I even tried a method which is "almost correct" and even that didn't work due to excessive math.

Well, my approach was this. We want to keep a certain speed constant. That means the distance the bullet travels per second needs to be the same all time. We have a function called y which gives us the height on a given x. This x is the distance (magnitude) from the starting point.

Let's say we already travelled something with our bullet and we are at a distance called d. We now are 1/60 (1 frame) further and we want to calculate our new function. This is not speed / 60 + d, because that means our horizontal speed is equal, which can't be true if our angle also changes. That means we need to get the new x (we call this e) in which the total distance the bullet has travelled is speed * 1/60. We call this dist.

We can get the length between two points via the integral calculus of:

math.sqrt(1 + (derive(y)^2)

Even for simple functions this is almost impossible to derive. For a sample function -x^2 + 8x Wolfram Alpha returns THIS as integral:

1/4 (2 (-4+x) sqrt(65-32 x+4 x^2)+sinh^(-1)(2 (-4+x)))

Well, at least it is an integral so we can work with that. The problem gets here, now. We call above function the arclen function. Integral math says that:

arclen(e) - arclen(d) = dist

So, if we want to get "e", we need to do:

arclen(e) = dist + arclen(d)

We can solve the stuff on the right. However, there is NO WAY for us to get an "inverse function" so we can get e of arclen. Trying to retrieve the function from Wolfram Alpha also gives no results. Conclusion: we have no way to find e. I think the function I provided (without trigonometry) already proves that this is extremely hard. You could try to create a brute forcer to solve this, but this will require too much CPU - you can't use your game for anything else besides some plotting of a bullet.

I hope you understood this a little bit. If the integral or derivation definitions confuse you, read some articles on them. Also "arc length" is a cool article to read on.